the {\itshape zimmer program} is a collection of conjectures and questions regarding actions of lattices in higher-rank simple lie groups on compact manifolds. for instance, it is conjectured that all non-trivial volume-preserving actions are built from algebraic examples using standard constructions. in particular, on manifolds whose dimension is below the dimension of all algebraic examples, {\itshape zimmer's conjecture} asserts that every action is finite. i will present some background, motivation, and selected previous results in the zimmer program. i will then explain two of my own results within the zimmer program: (1) a solution to zimmer's conjecture for actions of cocompact lattices in $sl(n,r), n>=3$ (joint with d. fisher and s. hurtado); (2) a classification (up to topological semiconjugacy) of lattice actions on tori whose induced action on homology satisfies certain criteria (joint with f. rodriguez hertz and z. wang).