Fully nonlinear potential flow (FNPF) models extend the regime of validity of linear potential flow models to include wave–body interactions in steep sea-states and/or involving large body displacements. More accurate predictions of wave kinematics, wave forces, and body motions can be obtained, compared to linear model predictions for interactions involving large free-surface and body displacements. First developed and widely applied in the fields of offshore engineering and naval hydrodynamics, such fully nonlinear models have only gradually been adopted in wave energy. The motivations of the development of fully nonlinear models, in the context of offshore engineering, are provided and linked to the fundamental principles of the models. Thereafter, a typical solution approach for the fully nonlinear model is described in some detail with emphasis on the free-surface tracking and body force computations. The heave response of a truncated cylinder, subject to a linear PTO in waves of various steepness, is examined before discussing the limitations of the model.