  We investigate the effects of disorder in Floquet topological insulators
(FTIs) occurring in semiconductor quantum wells. Such FTIs are induced by
resonantly driving a transition between the valence and conduction band. We
show that when disorder is added, the topological nature of such FTIs persists
as long as there is a mobility gap at the resonant quasi-energy. For strong
enough disorder, this gap closes and all the states become localized as the
system undergoes a transition to a trivial insulator. Interestingly, the
effects of disorder are not necessarily adverse: we show that in the same
quantum well, disorder can also induce a transition from a trivial to a
topological system, thereby establishing a Floquet Topological Anderson
Insulator (FTAI). We identify the conditions on the driving field necessary for
observing such a transition.
