Model predictive control (MPC) has achieved considerable success in the process industries, with its ability to deal with linear and nonlinear models, while observing system constraints and considering future behaviour. Given these characteristics, against the backdrop of the energy maximising control problem for Wave Energy Converters (WECs), with physical constraints on system variables and a non-causal optimal control solution it is, perhaps, natural to consider the application of MPC to the WEC problem. However, the WEC energy maximisation problem requires a significant modification of the traditional MPC objective function, resulting in a potentially non-convex optimisation problem. A variety of MPC formulations for WECs have been proposed, with variations in the WEC model, discretisation method, objective function and optimisation algorithm employed. This paper attempts to provide a critical comparison of the various WEC MPC algorithms, while also presenting WEC MPC algorithms within the broader context of other WEC “optimal” control schemes.