Biharmonic maps are critical points of bioenergy functional. Biharmonic submanifolds are submanifolds whose defining isometric immersions are biharmonic maps. Biharmonic maps generalize the notion of harmonic maps whilst biharmonic submanifolds includes minimal submaifolds as special cases. The talk will present some of our current work on biharmonic pseudo-Riemannian submanifolds after a brief survey of recent development of biharmonic submanifolds of Riemannian ambient spaces. This is a joint work with Yuxin Dong.