I will discuss the open system dynamics and steady states of two dimensional Floquet topological insulators: systems in which a topological Floquet-Bloch spectrum is induced by an external periodic drive. I will present a solution for the bulk and edge state carrier distributions, which takes into account energy and momentum relaxation through radiative recombination and electron-phonon interactions, as well as coupling to an external fermionic reservoir. The resulting steady state resembles a topological insulator in the Floquet basis. The particle distribution in the Floquet edge modes exhibits a sharp feature akin to the Fermi level in equilibrium systems, while the bulk hosts a small density of excitations. Using these distributions, I will analyze the regimes where edge-state transport can be observed. These results show that signatures of the non-trivial topology persist in the non-equilibrium steady state.