Uri Bader Weizmann Institute of Science I will start by surveying Margulis' Super-Rigidity and Zimmer's cocyle Super-Rigidity. I will then explain a method developed with Alex Furman, which allows to prove various extensions of these theorems. In the last part of the talk I will focus on some applications to groups which act on affine buildings. I will sketch some open problems regarding such groups, related to the Zimmer conjecture.