What is a Time Crystal?

The defining feature of a time crystal is that it exhibits subharmonic oscillations, but so do many other things in nature. In this talk, my main goal is to sharpen the question surrounding time crystals, and to provide some answers in the context of both classical and quantum many-body systems. Particular care will be taken to contextualize modern results on discrete time crystals with related phenomena in non-linear dynamical systems. Finally, we will demonstrate that locally-interacting, periodically-driven Hamiltonian dynamics coupled to a Langevin bath support finite-temperature discrete time crystals with an infinite auto-correlation time. I will end by surveying recent experiments demonstrating the observation of time crystalline order in a variety of quantum simulation platforms.