We study the long-time behaviour of many-body Floquet systems--many-body quantum systems under temporally periodic driving, arguably the simplest deviation from equilibrium.

We begin by showing that generically such interacting systems heat up, then focus on two ways to prevent this: integrability and disorder. We show that the nontrivial steady states thus achieved may host nontrivial phases and focus on the recently observed example of "time crystals". Finally we close with some remarks on open floquet systems.