The design of controllers for wave energy devices has evolved from early monochromatic impedance-matching methods to complex numerical algorithms that can handle panchromatic seas, constraints, and nonlinearity. However, the potential high performance of such numerical controller comes at a computational cost, with some algorithms struggling to implement in real-time, and issues surround convergence of numerical optimisers. Within the broader area of control engineering, practitioners have always displayed a fondness for simple and intuitive controllers, as evidenced by the continued popularity of the ubiquitous PID controller. Recently, a number of energy-maximising wave energy controllers have been developed based on relatively simple strategies, stemming from the fundamentals behind impedance-matching. This paper documents this set of (5) controllers, which have been developed over the period 2010–2020, and compares and contrasts their characteristics, in terms of energy-maximising performance, the handling of physical constraints, and computational complexity. The comparison is carried out both analytically and numerically, including a detailed case study, when considering a state-of-the-art CorPower-like device.