a remarkable phenomenon discovered by g.a.margulis in the 1970s, now called super-rigidity, concerns linear representations of discrete subgroups groups in such groups as sl(3,r). as one of the applications of super-rigidity margulis proved arithmeticity of these groups. in the 1980s r.j.zimmer extended margulis' work to the context of cocycles, that found many applications in ergodic theory and geometry of actions on manifolds. in the talk i plan to give a broad overview of some of these topics and discuss some recent developments.