The wave energy sector has made and is still doing a great effort in order to open up a niche in the energy market, working on several and diverse concepts and making advances in all aspects towards more efficient technologies. However, economic viability has not been achieved yet, for which maximisation of power production over the full range of sea conditions is crucial. Precise mathematical models are essential to accurately reproduce the behaviour, including nonlinear dynamics, and understand the performance of wave energy converters. Therefore, nonlinear models must be considered, which are required for power absorption assessment, simulation of devices motion and model-based control systems. Main sources of nonlinear dynamics within the entire chain of a wave energy converter - incoming wave trains, wave-structure interaction, power take-off systems or mooring lines- are identified, with especial attention to the wave-device hydrodynamic interaction, and their influence is studied in the present paper for different types of converters. In addition, different approaches to model nonlinear wave-device interaction are presented, highlighting their advantages and drawbacks. Besides the traditional Navier-Stokes equations or potential flow methods, 'new' methods such as system-identification models, smoothed particle hydrodynamics or nonlinear potential flow methods are analysed.