Wave energy has a significant part to play in providing a carbon-free solution to the world’s increasing appetite for energy. In many countries, there is sufficient wave energy to cater for the entire national demand, and wave energy also has some attractive features in being relatively uncorrelated with wind, solar and tidal energy, easing the renewable energy dispatch problem. However, wave energy has not yet reached commercial viability, despite the first device designs being proposed in 1898. Control technology can play a major part in the drive for economic viability of wave energy and this paper charts the progress made since the first wave energy control systems were suggested in the 1970s, and examines current outstanding challenges for the control community.