How does a C++ reference look, memory-wise?

everywhere the reference j is encountered, it is replaced with the address of i. So basically the reference content address is resolved at compile time, and there is not need to dereference it like a pointer at run time.

Just to clarify what I mean by the address of i :

void function(int& x)
{
    x = 10;
}

int main()
{
    int i = 5;
    int& j = i;

    function(j);
}

In the above code, j should not take space on the main stack, but the reference x of function will take a place on its stack. That means when calling function with j as an argument, the address of i that will be pushed on the stack of function. The compiler can and should not reserve space on the main stack for j.

For the array part the standards say ::

C++ Standard 8.3.2/4:

There shall be no references to references, no arrays of references, and no pointers to references.

Why arrays of references are illegal?

How does a C++ reference look, memory-wise?

It doesn't. The C++ standard only says how it should behave, not how it should be implemented.

In the general case, compilers usually implement references as pointers. But they generally have more information about what a reference may point to, and use that for optimization.

Remember that the only requirement for a reference is that it behaves as an alias for the referenced object. So if the compiler encounters this code:

int i = 42;
int& j = i;
int k = 44;

what it sees is not "create a pointer to the variable i" (although that is how the compiler may choose to implement it in some cases), but rather "make a note in the symbol table that j is now an alias for i."

The compiler doesn't have to create a new variable for j, it simply has to remember that whenever j is referenced from now on, it should really swap it out and use i instead.

As for creating an array of references, you can't do it because it'd be useless and meaningless.

When you create an array, all elements are default-constructed. What does it mean to default-construct a reference? What does it point to? The entire point in references is that they re initialized to reference another object, after which they can not be reseated.

So if it could be done, you would end up with an array of references to nothing. And you'd be unable to change them to reference something because they'd been initialized already.

In practice, a reference is equivalent to a pointer, except that the extra constraints on how references are allowed to be used can allow a compiler to "optimize it away" in more cases (depending on how smart the compiler is, its optimization settings, etc etc of course).

You can't define an array of references because there is no syntax to initialize them. C++ does not allow uninitialized references. As for your first question, the compiler is under no obligation to allocate space for unnecessary variables. There is no way to have j point to another variable, so it's effectively just an alias for i in the function's scope, and that's how the compiler treats it.

Something that is only mentioned in passing elsewhere - how to get the compiler to devote some storage space to a reference:

class HasRef
{
    int &r;

public:
    HasRef(int &n)
        : r(n) { }
};

This denies the compiler the opportunity to simply treat it as a compile-time alias (an alternative name for the same storage).

References don't actually exist physically until they need to have a physical manifestation (i.e., as a member of an aggregate).

Having an array of references is illegal probably due to the above. But nothing prevents you from creating an array of structs/classes that have reference members.

I'm sure someone will point out the standard clause that mentions all this.

It's not fixed - the compiler has a great freedom in how to implement a reference on a case by case basis. So in your second example it treats j as an alias for i, nothing else needed. When passing a ref parameter it could also use a stack-offset, again no overhead. But in other situations it could use a pointer.

Most about what a reference is and why and how storage for it can be optimized away by the compiler has already been said in other answers. However, in some comments it was incorrectly stated, that for reference variables (in contrast to reference arguments in functions) the reference is always just an alias and never needs extra memory. This is true if the reference always refers to the same variable. However, if the reference can refer to different memory locations and the compiler cannot determine in advance to which one, it will need to allocate memory for it, like in the following example:

#include <ctime>
#include <iostream>
int i = 2;
int j = 3;
int& k = std::time(0)%2==1 ? i : j;

int main(){
    std::cout << k << std::endl;
}

If you try this on godbolt (https://godbolt.org/z/38x1Eq83o) you will see, that e.g. gcc on x86-64 will reserve 8 bytes for k in order to store a pointer to either i or j depending on the return value of std::time.