We present the classical ergodic theorems due to von Neumann and Birkhoff, along with some of their extensions such as the uniform ergodic theorem for uniquely ergodic systems and the polynomial mean ergodic theorem. We also prove the multiple ergodic theorem for weakly mixing systems and systems with discrete spectrum. On the way we present an important tool known as the van der Corput trick. The chapter ends with an overview of some related results and research directions.