Appears in collection : Group Actions and Rigidity: Around the Zimmer Program / Actions de Groupes et Rigidité : Autour du programme de Zimmer

We introduce Margulis' and Zimmer's superrigidity. Statements give heuristics in Zimmer program, that is higher rank lattice actions on smooth manifolds. After we state the statement, we mainly focus how it interacts with group actions. Finally, we will also discuss about open questions.