In this talk I will briefly review the Floquet theory describing periodically driven systems. I will focus on high frequency limits, where one can obtain Floquet Hamiltonians perturbatively in the inverse frequency using the Magnus expansion. I will then discuss classes of driving protocols, where one can get non-trivial high frequency limits and illustrate them with examples such as the famous Kapitza pendulum and recently realized artificial magnetic fields in MIT and Munich groups. At the end I will discuss convergence of the Magnus expansion, connection with the many-body localization in the energy space and possible implications for digital quantum computing.