Closures: why are they so useful?
As an OO developer, maybe I have difficulty seeing its value. What added value do they give? Do they fit in an OO world?
Answer
You can see it as a generalization of a class.
Your class holds some state. It has some member variables that its methods can use.
A closure is simply a more convenient way to give a function access to local state.
Rather than having to create a class which knows about the local variable you want the function to use, you can simply define the function on the spot, and it can implicitly access every variable that is currently visible.
When you define a member method in a traditional OOP language, its closure is "all the members visible in this class".
Languages with "proper" closure support simply generalize this, so a function's closure is "all the variables visible here". If "here" is a class, then you have a traditional class method.
If "here" is inside another function, then you have what functional programmers think of as a closure. Your function can now access anything that was visible in the parent function.
So it's just a generalization, removing the silly restriction that "functions can only be defined inside classes", but keeping the idea that "functions can see whatever variables are visible at the point where they're declared".