Abstract: Quantum dynamics of a periodically driven system is described in terms of the Floquet states. Generally, if the system is in a Floquet state, its dynamical variables oscillate with the period of the driving. Recently much interest have attracted systems where this discrete time-translation symmetry is broken, the “time crystal” effect. Nonlinear oscillators, including nanomechanical systems and modes in electromagnetic cavities, provide a natural platform for studying this effect. I will discuss the classical and quantum phase transitions to the broken-symmetry state in systems of coupled oscillators. Time permitting, and for completeness, I will also show time-symmetry breaking in the simplest quantum system, a qubit.