Non-equilibrium systems can exhibit phenomena fundamentally richer than their static counterparts. Indeed, certain phases of matter that are provably forbidden in equilibrium, such as quantum time crystals, have found new life in out-of-equilibrium systems. In this talk, I will describe recent advances, which predict the spontaneous breaking of time translation symmetry in periodically driven quantum systems. The resulting discrete time crystal exhibits collective oscillations — arising from a combination of many-body synchronization and localization — that are quantized to an integer multiple of the drive period. I will describe a simple model for a one dimensional discrete time crystal, which explicitly reveals the rigidity of the emergent oscillations as the drive is varied. Recent experimental realizations of discrete time crystalline order in long-range interacting trapped ions and solid-state spins will be discussed.