Closures: why are they so useful?

Question

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 1

As to the concluding query: "Do (closures) fit in an OO world?"

In many languages, closures, along with first-class functions, provide the very foundation for devising OO programs: Javascript, Lua and Perl come to mind.

In another more "traditional" OO language with which I'm familiar, Java, there are 2 primary differences:

1. Functions are not first class constructs
2. In Java the implementation details of OO (whether closures are used internally) is not exposed directly to the developer as it is in Javascript, Lua and Perl

Therefore in a "traditional OO" language such as Java, the addition of closures is largely just so much syntactic sugar.