The statistical mechanics of equilibrium systems is characterized by two fundamental ideas: that closed systems approach a late time thermal state and that of phase structure wherein such late time states exhibit singular changes as various parameters characterizing the system are changed. Recent progress has established generalizations of these ideas which apply to periodically driven, or Floquet, closed quantum systems. I will describe this progress, which centrally uses other recent advances in our understanding of many body localization. I will describe how it has resulted in the discovery of entirely new phases such as the π-spin glass/Floquet time crystal which exist only in driven quantum systems.