Abstract: Quantum many-body physics has traditionally focused on equilibrium properties and low-energy excitations. However, in recent years, motivated by novel experimental possibilities, the study of quantum matter far from equilibrium is emerging as an active and exciting field of research. In the absence of external mechanisms for reaching equilibrium, the behavior of an isolated quantum system poses many new challenges to our understanding of quantum matter. I will motivate the study of quantum dynamics in isolated systems, contrast with equilibrium physics and dissipative dynamics, and present a few examples of such dynamical phenomena. In particular, I will highlight the role and some properties of the many-body eigenspectrum.