  Equilibrium theormodynamics is characterized by two fundamental ideas:
thermalisation--that systems approach a late time thermal state; and phase
structure--that thermal states exhibit singular changes as various parameters
characterizing the system are changed. We summarise recent progress that has
established generalizations of these ideas to periodically driven, or Floquet,
closed quantum systems. This has resulted in the discovery of entirely new
phases which exist only out of equilibrium, such as the $\pi$-spin glass or
Floquet time crystal.
