The sustainable development of the offshore wind and wave energy sectors requires optimising the exploitation of the resources, and it is in relation to this and the shared challenge for both industries to reduce their costs that the option of integrating offshore wind and wave energy arose during the past decade. The relevant aspects of this integration are addressed in this work: the synergies between offshore wind and wave energy, the different options for combining wave and offshore wind energy, and the technological aspects. Because of the novelty of combined wave and offshore wind systems, a comprehensive classification was lacking. This is presented in this work based on the degree of integration between the technologies, and the type of substructure. This classification forms the basis for the review of the different concepts. This review is complemented with specific sections on the state of the art of two particularly challenging aspects, namely the substructures and the wave energy conversion.