Landau's idea of classifying phases of matter in terms of symmetry breaking is a cornerstone of modern physics. Ferromagnets or crystals, just to mention to simple cases, are example of this sort. Can time-translation invariance be spontaneously broken? The existence of time-crystals was first addressed by Wilczek, more than a decade ago, for quantum many-body systems launching an intense activity both theoretically and experimentally. Despite their conceptual simplicity and apparent similarity to ordinary crystals, they were experimentally observed only recently, eighty years after the Landau theory of symmetry breaking.
I will introduce the basic properties of time-crystals and briefly review the field focusing on many-body systems that are periodically driven. If time permits, I will also briefly address prospects to observe continuous time-crystals and their relation to quantum synchronisation.
