The programming paradigm that emphasizes immutability and function application is Functional Programming. This paradigm treats computation as the evaluation of mathematical functions and avoids changing state or mutable data. In functional programming, functions are first-class citizens, enabling higher-order functions and facilitating easier reasoning about code. This approach promotes cleaner, more modular code and is commonly seen in languages like Haskell, Scala, and JavaScript, particularly in modern frameworks that leverage functional techniques.