Driven quantum systems provide an intriguing landscape for studying novel phases of non-equilibrium matter. 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 that are quantized to an integer multiple of the drive period. Particular care will be taken to contextualize modern results on discrete time crystals with subharmonic oscillations that are commonplace in non-linear dynamical systems. Time permitting, I will survey recent experiments demonstrating the observation of time crystalline order in a variety of quantum simulation platforms.