Addressing the challenge of controlling charge and energy transfer in complex material systems requires theoretical methods that accurately described the coupling between electronic state transitions and nuclear dynamics, and that are computationally efficient for complex many-dimensional systems. In this talk, we introduce two recent approximate dynamic techniques developed in our group that leverage the computational efficiency of classical mechanics while incorporating quantum effects. We demonstrate the numerical accuracy of these methods in model systems and we discuss the challenges associated with extending their implementation to atomistic simulations of chemical reactions.