Functional programming is a programming paradigm that treats computation as the evaluation of mathematical functions and avoids changing-state and mutable data. Some key aspects of functional programming include: breaking problems down into smaller pure functions, using functions as first-class citizens that can be passed in and returned from other functions, avoiding side effects from functions, and embracing concepts like referential transparency. JavaScript supports functional programming with features like first-class functions, higher-order functions, immutability, and functional utilities like map and reduce. Functional programming can make code more readable, reusable, and easier to understand when working with larger teams or on larger applications.