Time-domain models are capable of dealing with the nonlinearities arising from the different elements of the energy chain as well as more complex formulations for fluid interaction and damping mechanisms that result in nonlinear hydrodynamic forces. Furthermore, they allow modelling transient situations that are impossible to characterize in a frequency-domain approach, which are applicable solely to stationary processes. This chapter presents an overall review of the main numerical techniques that are applicable to the solution of the dynamics of wave energy converters (WECs) in the time domain and that are based on the general formulation of the Cummins equation. Methods for the computation of wave excitation forces are presented with an insight into the randomness of the simulated wave signal and its consequence on the statistical properties of the results. The requirement for a convolution integral to be included in the equations of motion to account for radiation forces gives rise to a variety of approaches which are briefly presented and reviewed. The consequences of different choices on the numerical approach for time-domain analysis are illustrated by making reference to a simple type of WEC: a cylindrical point-absorber connected to either a linear or a hydraulic power take-off.