Non-equilibrium systems can exhibit phoenoma fundamentally richer than their static counterpars. For example, certain phases of matter that are provably forbidden in equilibrium systems. In this talk, I will begin by summarizing recent advances, which predicted the spontaneous breaking of time translation symmetry in periodically driven quantum systems and culminated in experimental observation of time crystals in two disparate systems. The resulting time crystal exhibits collective oscillations - arising from many-body synchronization - that are quantized to an interger multiple of the drive period. I will then describe two new examples of "surprising" time-translation symmetry breaking in one dimensional systems. The first will focus on long-range pre-thermal time crystals, which the second will address the possibility of classical time crystals.
