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We will discuss smooth actions on manifolds by lattices in SL(n,R) with n>2. Zimmer's program, motivated by superrigidity results of Margulis and Zimmer, aims to “classify” such actions. We expect to understand the manifold or the lattice from the action unless the action is trivial. When the dimension is at most n-1, recent works by Brown-Fisher-Hurtado and Brown-Rodriguez Hertz-Wang gave complete answers. In this case, we only see zero entropy actions, isometric or projective actions. In the talk, we give partial answers for actions on n-dimensional manifolds with “positive entropy” by lattices in SL(n,R), n>2. Part of the talk is based on an ongoing work with Aaron Brown.