Biharmonic maps are maps between Riemannian manifolds which are critical points of the bienergy functional. They include harmonic and biharmonic functions, geodesics, minimal surfaces and submanifolds, and harmonic maps as special examples which have important applications in theoretical physics and mathematics. The talk will begin with some basic concepts, examples, and fundamental problems in the study of biharmonic maps, and then focus on some of my recent work on the study of biharmonic hypersurfaces, the Generalized Chen’s Conjecture on biharmonic submanifolds, Biharmonic maps in two dimensions, and biharmonic Riemannian submersions.