In this paper, a literature review is presented regarding the hydrodynamic effects of different hand and arm movements during swimming with the aim to identify lacunae in current methods and knowledge, and to distil practical guidelines for coaches and swimmers seeking to increase swimming speed. Experimental and numerical studies are discussed, examining the effects of hand orientation, thumb position, finger spread, sculling movements, and hand accelerations during swimming, as well as unsteady properties of vortices due to changes in hand orientation. Collectively, the findings indicate that swimming speed may be increased by avoiding excessive sculling movements and by spreading the fingers slightly. In addition, it appears that accelerating the hands rather than moving them at constant speed may be beneficial, and that (in front crawl swimming) the thumb should be abducted during entry, catch, and upsweep, and adducted during the pull phase. Further experimental and numerical research is required to confirm these suggestions and to elucidate their hydrodynamic underpinnings and identify optimal propulsion techniques. To this end, it is necessary that the dynamical motion and resulting unsteady effects are accounted for, and that flow visualization techniques, force measurements, and simulations are combined in studying those effects.