The programming paradigm that emphasizes immutability and first-class functions is known as functional programming. This approach focuses on writing software by composing pure functions, avoiding shared state and mutable data. It encourages the use of higher-order functions and emphasizes recursion over traditional looping constructs. By promoting immutability, functional programming reduces side effects, making code easier to reason about, test, and maintain. Popular languages supporting this paradigm include Haskell, Scala, and JavaScript, significantly influencing modern software development practices.