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Equilibrium statistical mechanics rests on the assumption of ergodic dynamicsof a system modulo the conservation laws of local observables: extremization ofentropy immediately gives Gibbs' ensemble (GE) for energy conserving systemsand a generalized version of it (GGE) when the number of local conservedquantities (LCQ) is more than one. Through the last decade, statisticalmechanics has been extended to describe the late-time behaviour of periodicallydriven (Floquet) quantum matter starting from a generic state. The structurebuilt on the fundamental assumptions of ergodicity and identification of therelevant "conservation laws" in this inherently non-equilibrium setting. Morerecently, it has been shown that the statistical mechanics has a much richerstructure due to the existence of {\it emergent} conservation laws: these areapproximate but stable conservation laws arising {\it due to the drive}, andare not present in the undriven system. Extensive numerical and analyticalresults support perpetual stability of these emergent (though approximate)conservation laws, probably even in the thermodynamic limit. This banks on therecent finding of a sharp ergodicity threshold for Floquet thermalization inclean, interacting non-integrable Floquet systems. This opens up a newpossibility of stable Floquet engineering in such systems. This review intendsto give a theoretical overview of these developments. We conclude by brieflysurveying the experimental scenario.

Statistical Mechanics of Floquet Quantum Matter: Exact and Emergent Conservation Laws