Recent work has shown that manipulating a quantum system using a periodic drive provides a new means for externally controlling it. Such a periodic drive can give rise to topological states in trivial quantum wells, bulk semiconductors, and even in graphene; and it can also turn a quantum wire into a system which could have Majorana states - of two flavors. Hitting a quantum system (more so, periodically!), may suggest complications, however, such as heating. I will show that this can be avoided by tailoring the thermal bath in which the system is immersed. Altogether, we will find that there is much rich physics in Floquet quantum states and their close relatives, and that one can work with them to obtain useful, finite-entropy, many-body steady states.