For a manifold M, the Nielsen realization problem asks when a group of symmetries of the fundamental group π_1(M) is realized by a group of homeomorphisms of M. For surfaces, this problem was posed in different forms by Nielsen (1930s) and Thurston (1970s) and has connections to geometry, dynamics, and rigidity. This talk will focus on recent work on Nielsen realization for 3-manifolds. This is joint work with Lei Chen and Corey Bregman.