Wave-energy converters of the point-absorbing type (i.e., having small extension compared with the wavelength) are promising for achieving cost reductions and design improvements because of a high power-to-volume ratio and better possibilities for mass production of components and devices as compared with larger converter units. However, their frequency response tends to be narrow banded, which means that the performance in real seas (irregular waves) will be poor unless their motion is actively controlled. Only then the invested equipment can be fully exploited, bringing down the overall energy cost. In this work various control methods for point-absorbing devices are reviewed, and a representative selection of methods is investigated by numerical simulation in irregular waves, based on an idealized example of a heaving semisubmerged sphere. Methods include velocity-proportional control, approximate complex conjugated control, approximate optimal velocity tracking, phase control by latching and clutching, and model-predictive control, all assuming a wave pressure measurement as the only external input to the controller. The methods are applied for a single-degree-of-freedom heaving buoy. Suggestions are given on how to implement the controllers, including how to tune control parameters and handle amplitude constraints. Based on simulation results, comparisons are made on absorbed power, reactive power flow, peak-to-average power ratios, and implementation complexity. Identified strengths and weaknesses of each method are highlighted and explored. It is found that overall improvements in average absorbed power of about 100–330% are achieved for the investigated controllers as compared with a control strategy with velocity-proportional machinery force. One interesting finding is the low peak-to-average ratios resulting from clutching control for wave periods about 1.5 times the resonance period and above.