The coherent optical manipulation of solids is emerging as a promising way to engineer novel quantum states of matter. The strong time-periodic potential of intense laser light was predicted to generate hybrid photon–electron states named Floquet–Bloch states. In this talk, I will report on first experimental observation of these states in topological insulators (TI). Using time- and angle-resolved photoemission spectroscopy, we show that an intense ultrashort mid-infrared pulse with energy below the bulk band gap of TI hybridizes with the surface Dirac fermions of a topological insulator to form Floquet-Bloch bands. The photon-dressed surface band structure is composed of a manifold of Dirac cones evenly spaced by the photon energy and exhibits polarization-dependent band gaps at the avoided crossings of the Dirac cones. Circularly polarized photons induce an additional gap at the Dirac point, which is a signature of broken time-reversal symmetry on the surface. Beyond topological insulators, manipulation of electronic bands via light matter interaction holds great promise in many other systems as well. I will illustrate this with our recent measurements on monolayer semiconducting transition-metal dichalcogenides in which we were able to break valley degeneracy using off-resonant circularly polarized light