Ocean wave energy has been of interest since at least the mid-1970s and great advances in the understanding of the fundamental principles of wave energy extraction and converter modelling have been made using linear hydrodynamic analysis. This paper reviews efforts that have been made to use nonlinear hydrodynamics to analyse wave energy converter behaviour and performance. Both ‘partially nonlinear’ and fully nonlinear potential flow methods, as well as computational fluid dynamics methods solving the Navier–Stokes equations and smoothed particle hydrodynamics have been used for this purpose and are reviewed here. These more complex methods have been applied primarily to single devices, so array and mooring line interactions are not considered. While a number of studies have been performed in these areas and results are encouraging, further advances are required to give accurate prediction or reproduction of experimental results.