We show that the application of circularly polarized electromagnetic radiation on the surface of a Weyl semimetal can generate states at that surface. These states can be characterized by their surface momentum. The Floquet eigenvalues e(i theta) of these states come in complex conjugate pairs rather than being equal to +/- 1. If the amplitude of the radiation is small, we find some unusual bulk-boundary relations: the values of theta of the surface states lie at the extrema of the theta’s of the bulk system, and the peaks of the Fourier transforms of the surface state wave functions lie at the momenta where the bulk theta’s have extrema. For the case of zero surface momentum, we can analytically derive scaling relations between the decay length of the surface states and the amplitude and penetration length of the radiation. For topological insulators, we again find that circularly polarized radiation can generate states on the top surface; these states have much larger decay lengths than the surface states which are present even in the absence of radiation. Finally, we show that radiation can generate surface states for trivial insulators also.