This article presents the methodology we have developed for the simulation of hydrogen transfer reactions, including multiple proton transfer and proton-coupled electron transfer reactions. The central method discussed is molecular dynamics with quantum transitions (MDQT), which is a mixed quantum/classical surface hopping method that incorporates nonadiabatic transitions between the proton vibrational and/or electronic states. The advantages of MDQT are that it accurately describes branching processes (i.e., processes involving multiple pathways), is valid in the adiabatic and nonadiabatic Limits and the intermediate regime, and provides realtime dynamical information. The multiconfigurational MDQT (MC-MDQT) method combines MDQT with an MC-SCF formulation of the vibrational modes for the simulation of processes involving multiple quantum modes (e.g., for multiple proton transfer reactions). MC-MDQT incorporates the significant correlation between the quantum modes in a computationally practical way and has been applied to proton transport along water chains. The EV-MDQT method incorporates transitions between mixed electronic/proton vibrational adiabatic states, which are calculated in a way that removes the standard double adiabatic approximation. EV-MDQT has been applied to model proton-coupled electron transfer reactions. These new developments allow the simulation of a wide range of biologically and chemically important hydrogen transfer processes.