There has been a revolution in the last few years in quantum simulation. The purpose of this talk is to provide an overview of these recent developments. Specifically, I will review Trotter-Suzuki simulation methods and discuss recent work that provides tighter estimates for the error in such approximations. I will then discuss truncated Dyson series simulations for time-dependent Hamiltonians before giving a discussion of qubitization. I will then conclude by discussing current open problems in quantum simulation and the strategies that may be needed to solve them.