Scala: when exactly are function parameter types required?

There are many ways functions can be defined in Scala, which leads to confusion about when exactly function parameter types are required. I usually start with the simplest possible definition and work my way down until compiler errors go away. I'd rather actually understand how this works.

For example:

_ + _

(x, y) => x + y

(x: Int, y: Int) => x + y

def sum(x: Int, y: Int) = x + y // as pointed out, this is a method,
                                // which not a function

Bonus points for a link to the documentation.