In this article, a range of problems and theories will be introduced which will build towards a new wave energy converter (WEC) concept with the acronym ‘ROTA’ standing for resonant over-topping absorber. First, classical results for wave power absorption for WECs constrained to operate in a single degree of freedom will be reviewed and the role of resonance in their operation highlighted. Emphasis will then be placed on how the introduction of further resonances can improve power take-off characteristics by extending the range of frequencies over which the efficiency is close to a theoretical maximum. Methods for doing this in different types of WECs will be demonstrated. Coupled resonant absorbers achieve this by connecting a WEC device equipped with its own resonance (determined from a hydrodynamic analysis) to a new system having separate mass/spring/damper characteristics. It is shown that a coupled resonant effect can be realized by inserting a water tank into a WEC and this idea forms the basis of the ROTA device. In essence, the idea is to exploit the coupling between the natural sloshing frequencies of the water in the internal tank and the natural resonance of a submerged buoyant circular cylinder device which is tethered to the sea floor allowing a rotary motion about its axis of attachment.