In this talk, I will discuss two different aspects of time-periodic (Floquet) systems.  In the first, I will show how group theory can be applied to periodically-driven systems to impose selection rules on non-linear optical processes.  In the second, I will discuss how a sudden quench into a superconducting state can give rise to large-scale Higgs oscillations, and how those, in turn, affect the optical properties of the material.