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Tidal disruption events involve numerous physical processes (fluid dynamics, magnetohydrodynamics, radiation transport, self-gravity, general relativistic dynamics) in highly nonlinear ways, and, because TDEs are transients by definition, frequently in non-equilibrium states. For these reasons, numerical solution of the relevant equations can be an essential tool for studying these events. In this chapter, we present a summary of the key problems of the field for which simulations offer the greatest promise and identify the capabilities required to make progress on them. We then discuss what has been---and what cannot be---done with existing numerical methods. We close with an overview of what methods now under development may do to expand our ability to understand these events.