Recently, there has been much interest in non-equilibrium phenomena in cold atomic gases and condensed matter systems. An important class of non-equilibrium systems includes those subjected to periodic drive, such as cold atoms in an optical lattice with periodically modulated parameters, or a solid state system with an incident laser beam. In this talk, I will describe some of our recent theoretical work aimed at finding accurate effective Hamiltonians for general periodically driven systems, including those with interactions. I will describe a “flow equation approach” inspired by renormalization group-type ideas that provides a useful description for highly accurate effective Hamiltonians. The method also serves as an anchor point for a wide range of approximate, physically motivated treatments of obtaining the effective Hamiltonian. I will also describe complementary work aimed at finding accurate Floquet Hamiltonians in the low-frequency, low-drive intensity limit.