Spontaneous symmetry-breaking is a fundamental concept in physics that underpins much of our understanding of equilibrium phases of matter, such as the sharp distinction between a solid crystalline phase and a liquid phase arising from spontaneously broken spatial translational symmetry. Recently, it was realized that time-translational symmetry can also be spontaneously broken [1,2]. More precisely, periodically-driven (Floquet) disordered interacting many-body systems may exhibit such a phenomenon -- in such systems, physical observables exhibit robust oscillations that is an integer multiple of the driving period T -- leading to a novel, nonequilibrium phase of matter dubbed a ``discrete time crystal" (DTC). In this talk, I will introduce the idea of discrete time crystals, and discuss the key concepts involved in defining this new nonequilibrium phase of matter. I will also explain the mechanism by which the DTC phase is stabilized, such as many-body localization (MBL) or `critically-slow' thermalization in disordered long-range systems , thereby providing an explanation for the recent experimental observation of robust DTC order in a diamond sample with NV-center impurities .
 Else, D., Bauer, B. and Nayak, C., Phys. Rev. Lett (117) 090402 (2016)
 von Keyserlingk, C.W., Khemani, V. and Sondhi, S., Phys. Rev. B (94) 085112 (2016)
 Ho, W. W., Choi, S., Lukin, M., and Abanin, D., Phys. Rev. Lett (119) 010602 (2017)
 Choi, S. et al., Nature 543, 221225 (2017)