  Topological insulators represent unique phases of matter with insulating bulk
and conducting edge or surface states, immune to small perturbations such as
backscattering due to disorder. This stems from their peculiar band structure,
which provides topological protections. While conventional tools (pressure,
doping etc.) to modify the band structure are available, time periodic
perturbations can provide tunability by adding time as an extra dimension
enhanced to the problem. In this short review, we outline the recent research
on topological insulators in non equilibrium situations. Firstly, we introduce
briefly the Floquet formalism that allows to describe steady states of the
electronic system with an effective time-independent Hamiltonian. Secondly, we
summarize recent theoretical work on how light irradiation drives semi-metallic
graphene or a trivial semiconducting system into a topological phase. Finally,
we show how photons can be used to probe topological edge or surface states.
