The syntax is:

a[start:stop]  # items start through stop-1
a[start:]      # items start through the rest of the array
a[:stop]       # items from the beginning through stop-1
a[:]           # a copy of the whole array

There is also the step value, which can be used with any of the above:

a[start:stop:step] # start through not past stop, by step

The key point to remember is that the :stop value represents the first value that is not in the selected slice. So, the difference between stop and start is the number of elements selected (if step is 1, the default).

The other feature is that start or stop may be a negative number, which means it counts from the end of the array instead of the beginning. So:

a[-1]    # last item in the array
a[-2:]   # last two items in the array
a[:-2]   # everything except the last two items

Similarly, step may be a negative number:

a[::-1]    # all items in the array, reversed
a[1::-1]   # the first two items, reversed
a[:-3:-1]  # the last two items, reversed
a[-3::-1]  # everything except the last two items, reversed

Python is kind to the programmer if there are fewer items than you ask for. For example, if you ask for a[:-2] and a only contains one element, you get an empty list instead of an error. Sometimes you would prefer the error, so you have to be aware that this may happen.

Relationship with the slice object

A slice object can represent a slicing operation, i.e.:

a[start:stop:step]

is equivalent to:

a[slice(start, stop, step)]

Slice objects also behave slightly differently depending on the number of arguments, similarly to range(), i.e. both slice(stop) and slice(start, stop[, step]) are supported. To skip specifying a given argument, one might use None, so that e.g. a[start:] is equivalent to a[slice(start, None)] or a[::-1] is equivalent to a[slice(None, None, -1)].

While the :-based notation is very helpful for simple slicing, the explicit use of slice() objects simplifies the programmatic generation of slicing.

The Python tutorial talks about it (scroll down a bit until you get to the part about slicing).

The ASCII art diagram is helpful too for remembering how slices work:

 +---+---+---+---+---+---+
 | P | y | t | h | o | n |
 +---+---+---+---+---+---+
 0   1   2   3   4   5   6
-6  -5  -4  -3  -2  -1

One way to remember how slices work is to think of the indices as pointing between characters, with the left edge of the first character numbered 0. Then the right edge of the last character of a string of n characters has index n.

Enumerating the possibilities allowed by the grammar for the sequence x:

>>> x[:]                # [x[0],   x[1],          ..., x[-1]    ]
>>> x[low:]             # [x[low], x[low+1],      ..., x[-1]    ]
>>> x[:high]            # [x[0],   x[1],          ..., x[high-1]]
>>> x[low:high]         # [x[low], x[low+1],      ..., x[high-1]]
>>> x[::stride]         # [x[0],   x[stride],     ..., x[-1]    ]
>>> x[low::stride]      # [x[low], x[low+stride], ..., x[-1]    ]
>>> x[:high:stride]     # [x[0],   x[stride],     ..., x[high-1]]
>>> x[low:high:stride]  # [x[low], x[low+stride], ..., x[high-1]]

Of course, if (high-low)%stride != 0, then the end point will be a little lower than high-1.

If stride is negative, the ordering is changed a bit since we're counting down:

>>> x[::-stride]        # [x[-1],   x[-1-stride],   ..., x[0]    ]
>>> x[high::-stride]    # [x[high], x[high-stride], ..., x[0]    ]
>>> x[:low:-stride]     # [x[-1],   x[-1-stride],   ..., x[low+1]]
>>> x[high:low:-stride] # [x[high], x[high-stride], ..., x[low+1]]

Extended slicing (with commas and ellipses) are mostly used only by special data structures (like NumPy); the basic sequences don't support them.

>>> class slicee:
...     def __getitem__(self, item):
...         return repr(item)
...
>>> slicee()[0, 1:2, ::5, ...]
'(0, slice(1, 2, None), slice(None, None, 5), Ellipsis)'

The answers above don't discuss slice assignment. To understand slice assignment, it's helpful to add another concept to the ASCII art:

                +---+---+---+---+---+---+
                | P | y | t | h | o | n |
                +---+---+---+---+---+---+
Slice position: 0   1   2   3   4   5   6
Index position:   0   1   2   3   4   5

>>> p = ['P','y','t','h','o','n']
# Why the two sets of numbers:
# indexing gives items, not lists
>>> p[0]
 'P'
>>> p[5]
 'n'

# Slicing gives lists
>>> p[0:1]
 ['P']
>>> p[0:2]
 ['P','y']

One heuristic is, for a slice from zero to n, think: "zero is the beginning, start at the beginning and take n items in a list".

>>> p[5] # the last of six items, indexed from zero
 'n'
>>> p[0:5] # does NOT include the last item!
 ['P','y','t','h','o']
>>> p[0:6] # not p[0:5]!!!
 ['P','y','t','h','o','n']

Another heuristic is, "for any slice, replace the start by zero, apply the previous heuristic to get the end of the list, then count the first number back up to chop items off the beginning"

>>> p[0:4] # Start at the beginning and count out 4 items
 ['P','y','t','h']
>>> p[1:4] # Take one item off the front
 ['y','t','h']
>>> p[2:4] # Take two items off the front
 ['t','h']
# etc.

The first rule of slice assignment is that since slicing returns a list, slice assignment requires a list (or other iterable):

>>> p[2:3]
 ['t']
>>> p[2:3] = ['T']
>>> p
 ['P','y','T','h','o','n']
>>> p[2:3] = 't'
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: can only assign an iterable

The second rule of slice assignment, which you can also see above, is that whatever portion of the list is returned by slice indexing, that's the same portion that is changed by slice assignment:

>>> p[2:4]
 ['T','h']
>>> p[2:4] = ['t','r']
>>> p
 ['P','y','t','r','o','n']

The third rule of slice assignment is, the assigned list (iterable) doesn't have to have the same length; the indexed slice is simply sliced out and replaced en masse by whatever is being assigned:

>>> p = ['P','y','t','h','o','n'] # Start over
>>> p[2:4] = ['s','p','a','m']
>>> p
 ['P','y','s','p','a','m','o','n']

The trickiest part to get used to is assignment to empty slices. Using heuristic 1 and 2 it's easy to get your head around indexing an empty slice:

>>> p = ['P','y','t','h','o','n']
>>> p[0:4]
 ['P','y','t','h']
>>> p[1:4]
 ['y','t','h']
>>> p[2:4]
 ['t','h']
>>> p[3:4]
 ['h']
>>> p[4:4]
 []

And then once you've seen that, slice assignment to the empty slice makes sense too:

>>> p = ['P','y','t','h','o','n']
>>> p[2:4] = ['x','y'] # Assigned list is same length as slice
>>> p
 ['P','y','x','y','o','n'] # Result is same length
>>> p = ['P','y','t','h','o','n']
>>> p[3:4] = ['x','y'] # Assigned list is longer than slice
>>> p
 ['P','y','t','x','y','o','n'] # The result is longer
>>> p = ['P','y','t','h','o','n']
>>> p[4:4] = ['x','y']
>>> p
 ['P','y','t','h','x','y','o','n'] # The result is longer still

Note that, since we are not changing the second number of the slice (4), the inserted items always stack right up against the 'o', even when we're assigning to the empty slice. So the position for the empty slice assignment is the logical extension of the positions for the non-empty slice assignments.

Backing up a little bit, what happens when you keep going with our procession of counting up the slice beginning?

>>> p = ['P','y','t','h','o','n']
>>> p[0:4]
 ['P','y','t','h']
>>> p[1:4]
 ['y','t','h']
>>> p[2:4]
 ['t','h']
>>> p[3:4]
 ['h']
>>> p[4:4]
 []
>>> p[5:4]
 []
>>> p[6:4]
 []

With slicing, once you're done, you're done; it doesn't start slicing backwards. In Python you don't get negative strides unless you explicitly ask for them by using a negative number.

>>> p[5:3:-1]
 ['n','o']

There are some weird consequences to the "once you're done, you're done" rule:

>>> p[4:4]
 []
>>> p[5:4]
 []
>>> p[6:4]
 []
>>> p[6]
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
IndexError: list index out of range

In fact, compared to indexing, Python slicing is bizarrely error-proof:

>>> p[100:200]
 []
>>> p[int(2e99):int(1e99)]
 []

This can come in handy sometimes, but it can also lead to somewhat strange behavior:

>>> p
 ['P', 'y', 't', 'h', 'o', 'n']
>>> p[int(2e99):int(1e99)] = ['p','o','w','e','r']
>>> p
 ['P', 'y', 't', 'h', 'o', 'n', 'p', 'o', 'w', 'e', 'r']

Depending on your application, that might... or might not... be what you were hoping for there!

Below is the text of my original answer. It has been useful to many people, so I didn't want to delete it.

>>> r=[1,2,3,4]
>>> r[1:1]
[]
>>> r[1:1]=[9,8]
>>> r
[1, 9, 8, 2, 3, 4]
>>> r[1:1]=['blah']
>>> r
[1, 'blah', 9, 8, 2, 3, 4]

This may also clarify the difference between slicing and indexing.

And a couple of things that weren't immediately obvious to me when I first saw the slicing syntax:

>>> x = [1,2,3,4,5,6]
>>> x[::-1]
[6,5,4,3,2,1]

Easy way to reverse sequences!

And if you wanted, for some reason, every second item in the reversed sequence:

>>> x = [1,2,3,4,5,6]
>>> x[::-2]
[6,4,2]

After using it a bit I realise that the simplest description is that it is exactly the same as the arguments in a for loop...

(from:to:step)

Any of them are optional:

(:to:step)
(from::step)
(from:to)

Then the negative indexing just needs you to add the length of the string to the negative indices to understand it.

This works for me anyway...

I find it easier to remember how it works, and then I can figure out any specific start/stop/step combination.

It's instructive to understand range() first:

def range(start=0, stop, step=1):  # Illegal syntax, but that's the effect
    i = start
    while (i < stop if step > 0 else i > stop):
        yield i
        i += step

Begin from start, increment by step, do not reach stop. Very simple.

The thing to remember about negative step is that stop is always the excluded end, whether it's higher or lower. If you want same slice in opposite order, it's much cleaner to do the reversal separately: e.g. 'abcde'[1:-2][::-1] slices off one char from left, two from right, then reverses. (See also reversed().)

Sequence slicing is same, except it first normalizes negative indexes, and it can never go outside the sequence:

TODO: The code below had a bug with "never go outside the sequence" when abs(step)>1; I think I patched it to be correct, but it's hard to understand.

def this_is_how_slicing_works(seq, start=None, stop=None, step=1):
    if start is None:
        start = (0 if step > 0 else len(seq)-1)
    elif start < 0:
        start += len(seq)
    if not 0 <= start < len(seq):  # clip if still outside bounds
        start = (0 if step > 0 else len(seq)-1)
    if stop is None:
        stop = (len(seq) if step > 0 else -1)  # really -1, not last element
    elif stop < 0:
        stop += len(seq)
    for i in range(start, stop, step):
        if 0 <= i < len(seq):
            yield seq[i]

Don't worry about the is None details - just remember that omitting start and/or stop always does the right thing to give you the whole sequence.

Normalizing negative indexes first allows start and/or stop to be counted from the end independently: 'abcde'[1:-2] == 'abcde'[1:3] == 'bc' despite range(1,-2) == []. The normalization is sometimes thought of as "modulo the length", but note it adds the length just once: e.g. 'abcde'[-53:42] is just the whole string.

I use the "an index points between elements" method of thinking about it myself, but one way of describing it which sometimes helps others get it is this:

mylist[X:Y]

X is the index of the first element you want.
Y is the index of the first element you don't want.

This is just for some extra info... Consider the list below

>>> l=[12,23,345,456,67,7,945,467]

Few other tricks for reversing the list:

>>> l[len(l):-len(l)-1:-1]
[467, 945, 7, 67, 456, 345, 23, 12]

>>> l[:-len(l)-1:-1]
[467, 945, 7, 67, 456, 345, 23, 12]

>>> l[len(l)::-1]
[467, 945, 7, 67, 456, 345, 23, 12]

>>> l[::-1]
[467, 945, 7, 67, 456, 345, 23, 12]

>>> l[-1:-len(l)-1:-1]
[467, 945, 7, 67, 456, 345, 23, 12]

The rules of slicing are as follows:

[lower bound : upper bound : step size]

I- Convert upper bound and lower bound into common signs.

II- Then check if the step size is a positive or a negative value.

(i) If the step size is a positive value, upper bound should be greater than lower bound, otherwise empty string is printed. For example:

s="Welcome"
s1=s[0:3:1]
print(s1)

The output:

Wel

However if we run the following code:

s="Welcome"
s1=s[3:0:1]
print(s1)

It will return an empty string.

(ii) If the step size if a negative value, upper bound should be lesser than lower bound, otherwise empty string will be printed. For example:

s="Welcome"
s1=s[3:0:-1]
print(s1)

The output:

cle

But if we run the following code:

s="Welcome"
s1=s[0:5:-1]
print(s1)

The output will be an empty string.

Thus in the code:

str = 'abcd'
l = len(str)
str2 = str[l-1:0:-1]    #str[3:0:-1] 
print(str2)
str2 = str[l-1:-1:-1]    #str[3:-1:-1]
print(str2)

In the first str2=str[l-1:0:-1], the upper bound is lesser than the lower bound, thus dcb is printed.

However in str2=str[l-1:-1:-1], the upper bound is not less than the lower bound (upon converting lower bound into negative value which is -1: since index of last element is -1 as well as 3).

I personally think about it like a for loop:

a[start:end:step]
# for(i = start; i < end; i += step)

Also, note that negative values for start and end are relative to the end of the list and computed in the example above by given_index + a.shape[0].

Most of the previous answers clears up questions about slice notation.

The extended indexing syntax used for slicing is aList[start:stop:step], and basic examples are:

:

More slicing examples: 15 Extended Slices

The basic slicing technique is to define the starting point, the stopping point, and the step size—also known as stride.

First, we will create a list of values to use in our slicing.

Create two lists to slice. The first is a numeric list from 1 to 9 (List A). The second is also a numeric list, from 0 to 9 (List B):

A = list(range(1, 10, 1)) # Start, stop, and step
B = list(range(9))

print("This is List A:", A)
print("This is List B:", B)

Index the number 3 from A and the number 6 from B.

print(A[2])
print(B[6])

Basic Slicing

Extended indexing syntax used for slicing is aList[start:stop:step]. The start argument and the step argument both default to None—the only required argument is stop. Did you notice this is similar to how range was used to define lists A and B? This is because the slice object represents the set of indices specified by range(start, stop, step).

As you can see, defining only stop returns one element. Since the start defaults to none, this translates into retrieving only one element.

It is important to note, the first element is index 0, not index 1. This is why we are using 2 lists for this exercise. List A's elements are numbered according to the ordinal position (the first element is 1, the second element is 2, etc.) while List B's elements are the numbers that would be used to index them ([0] for the first element, 0, etc.).

With extended indexing syntax, we retrieve a range of values. For example, all values are retrieved with a colon.

A[:]

To retrieve a subset of elements, the start and stop positions need to be defined.

Given the pattern aList[start:stop], retrieve the first two elements from List A.

I don't think that the Python tutorial diagram (cited in various other answers) is good as this suggestion works for positive stride, but does not for a negative stride.

This is the diagram:

 +---+---+---+---+---+---+
 | P | y | t | h | o | n |
 +---+---+---+---+---+---+
 0   1   2   3   4   5   6
-6  -5  -4  -3  -2  -1

From the diagram, I expect a[-4,-6,-1] to be yP but it is ty.

>>> a = "Python"
>>> a[2:4:1] # as expected
'th'
>>> a[-4:-6:-1] # off by 1
'ty'

What always work is to think in characters or slots and use indexing as a half-open interval -- right-open if positive stride, left-open if negative stride.

This way, I can think of a[-4:-6:-1] as a(-6,-4] in interval terminology.

 +---+---+---+---+---+---+
 | P | y | t | h | o | n |
 +---+---+---+---+---+---+
   0   1   2   3   4   5  
  -6  -5  -4  -3  -2  -1

 +---+---+---+---+---+---+---+---+---+---+---+---+
 | P | y | t | h | o | n | P | y | t | h | o | n |
 +---+---+---+---+---+---+---+---+---+---+---+---+
  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5  

I got a little frustrated in not finding an online source, or Python documentation that describes precisely what slicing does.

I took Aaron Hall's suggestion, read the relevant parts of the CPython source code, and wrote some Python code that performs slicing similarly to how it's done in CPython. I've tested my code in Python 3 on millions of random tests on integer lists.

You may find the references in my code to the relevant functions in CPython helpful.

def slicer(x, start=None, stop=None, step=None):
    """ Return the result of slicing list x.  

    See the part of list_subscript() in listobject.c that pertains 
    to when the indexing item is a PySliceObject.
    """

    # Handle slicing index values of None, and a step value of 0.
    # See PySlice_Unpack() in sliceobject.c, which
    # extracts start, stop, step from a PySliceObject.
    maxint = 10000000       # A hack to simulate PY_SSIZE_T_MAX
    if step is None:
        step = 1
    elif step == 0:
        raise ValueError('slice step cannot be zero')

    if start is None:
        start = maxint if step < 0 else 0
    if stop is None:
        stop = -maxint if step < 0 else maxint

    # Handle negative slice indexes and bad slice indexes.
    # Compute number of elements in the slice as slice_length.
    # See PySlice_AdjustIndices() in sliceobject.c
    length = len(x)
    slice_length = 0

    if start < 0:
        start += length
        if start < 0:
            start = -1 if step < 0 else 0
    elif start >= length:
        start = length - 1 if step < 0 else length

    if stop < 0:
        stop += length
        if stop < 0:
            stop = -1 if step < 0 else 0
    elif stop > length:
        stop = length - 1 if step < 0 else length

    if step < 0:
        if stop < start:
            slice_length = (start - stop - 1) // (-step) + 1
    else:
        if start < stop:
            slice_length = (stop - start - 1) // step + 1

    # Cases of step = 1 and step != 1 are treated separately
    if slice_length <= 0:
        return []
    elif step == 1:
        # See list_slice() in listobject.c
        result = []
        for i in range(stop - start):
            result.append(x[i+start])
        return result
    else:
        result = []
        cur = start
        for i in range(slice_length):
            result.append(x[cur])
            cur += step
        return result

It is easy to understand if we could relate slicing to range, which gives the indexes. We can categorize slicing into the following two categories:

1. No step or step > 0. For example, [i:j] or [i:j:k] (k>0)

Suppose the sequence is s=[1,2,3,4,5].

• if 0<i<len(s) and 0<j<len(s), then [i:j:k] -> range(i,j,k)

For example, [0:3:2] -> range(0,3,2) -> 0, 2

• if i>len(s) or j>len(s), then i=len(s) or j=len(s)

For example, [0:100:2] -> range(0,len(s),2) -> range(0,5,2) -> 0, 2, 4

• if i<0 or j<0, then i=max(0,len(s)+i) or j=max(0,len(s)+j)

For example, [0:-3:2] -> range(0,len(s)-3,2) -> range(0,2,2) -> 0

For another example, [0:-1:2] -> range(0,len(s)-1,2) -> range(0,4,2) -> 0, 2

• if i is not specified, then i=0

For example, [:4:2] -> range(0,4,2) -> range(0,4,2) -> 0, 2

• if j is not specified, then j=len(s)

For example, [0::2] -> range(0,len(s),2) -> range(0,5,2) -> 0, 2, 4

2. Step < 0. For example, [i:j:k] (k<0)

Suppose the sequence is s=[1,2,3,4,5].

• if 0<i<len(s) and 0<j<len(s), then [i:j:k] -> range(i,j,k)

For example, [5:0:-2] -> range(5,0,-2) -> 5, 3, 1

• if i>len(s) or j>len(s), then i=len(s)-1 or j=len(s)-1

For example, [100:0:-2] -> range(len(s)-1,0,-2) -> range(4,0,-2) -> 4, 2

• if i<0 or j<0, then i=max(-1,len(s)+i) or j=max(-1,len(s)+j)

For example, [-2:-10:-2] -> range(len(s)-2,-1,-2) -> range(3,-1,-2) -> 3, 1

• if i is not specified, then i=len(s)-1

For example, [:0:-2] -> range(len(s)-1,0,-2) -> range(4,0,-2) -> 4, 2

• if j is not specified, then j=-1

For example, [2::-2] -> range(2,-1,-2) -> 2, 0

For another example, [::-1] -> range(len(s)-1,-1,-1) -> range(4,-1,-1) -> 4, 3, 2, 1, 0

In summary

The important idea to remember about indices of a sequence is that

• nonnegative indices begin at the first item in the sequence;
• negative indices begin at the last item in the sequence (so only apply to finite sequences).

In other words, negative indices are shifted right by the length of the sequence:

              0   1   2   3   4   5   6   7   ...
            -------------------------
            | a | b | c | d | e | f |
            -------------------------
...  -8  -7  -6  -5  -4  -3  -2  -1

With that in mind, subscription and slicing are straightforward.

Subscription

Subscription uses the following syntax:*

sequence[index]

Subscription selects a single item in the sequence at index:

>>> 'abcdef'[0]
'a'
>>> 'abcdef'[-6]
'a'

Subscription raises an IndexError for an index that is out of range:

>>> 'abcdef'[100]
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
IndexError: string index out of range

Slicing

Slicing uses the following syntax:**

sequence[start:stop:step]

Slicing selects a range of items in the sequence, beginning at start inclusive and ending at stop exclusive:

>>> 'abcdef'[0:2:1]
'ab'
>>> 'abcdef'[0:-4:1]
'ab'
>>> 'abcdef'[-6:-4:1]
'ab'
>>> 'abcdef'[-6:2:1]
'ab'
>>> 'abcdef'[1:-7:-1]
'ba'
>>> 'abcdef'[-5:-7:-1]
'ba'

Slicing defaults to the fullest range of items in the sequence, so it uses the following default values for any start, stop, or step that is omitted or equal to None:***

• step defaults to 1;
• if step is positive
  • start defaults to 0 (first item index),
  • stop defaults to start + len(sequence) (last item index plus one);
• if step is negative
  • start defaults to -1 (last item index),
  • stop defaults to start - len(sequence) (first item index minus one).

>>> 'abcdef'[0:6:1]
'abcdef'
>>> 'abcdef'[::]
'abcdef'
>>> 'abcdef'[-1:-7:-1]
'fedcba'
>>> 'abcdef'[::-1]
'fedcba'

Slicing raises a ValueError for a step that is equal to zero:

>>> 'abcdef'[::0]
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: slice step cannot be zero

Slicing does not raise an IndexError for a start or stop that is out of range (contrary to subscription):

>>> 'abcdef'[-100:100]
'abcdef'

* The expressions sequence[index] and sequence.__getitem__(index) are equivalent.

** The expressions sequence[start:stop:step], sequence[slice(start, stop, step)], and sequence.__getitem__(slice(start, stop, step)) are equivalent, where the built-in class slice instance packs start, stop, and step.

*** The expressions sequence[:], sequence[::], and sequence[None:None:None] use default values for start, stop, and step.

Lots of answers already, but I wanted to add a performance comparison

~$ python3.8 -m timeit -s 'fun = "this is fun;slicer = slice(0, 3)"' "fun_slice = fun[slicer]" 
10000000 loops, best of 5: 29.8 nsec per loop
~$ python3.8 -m timeit -s 'fun = "this is fun"' "fun_slice = fun[0:3]" 
10000000 loops, best of 5: 37.9 nsec per loop
~$ python3.8 -m timeit -s 'fun = "this is fun"' "fun_slice = fun[slice(0, 3)]" 
5000000 loops, best of 5: 68.7 nsec per loop
~$ python3.8 -m timeit -s 'fun = "this is fun"' "slicer = slice(0, 3)" 
5000000 loops, best of 5: 42.8 nsec per loop

So, if you are using the same slice repeatedly, it would be beneficial and improve readability to use a slice object. However, if you are slicing only a handful of times, [:] notation should be preferred.

Here's a simple mnemonic for remembering how it works:

• S L *I* C *E*
• the 'i' of slice comes first and stands for inclusive,
• the 'e' comes last and stands for exclusive.

So array[j:k] will include the jth element and exclude the kth element.