This article presents a brief review of past and present ideas regarding the possible mechanisms by which swimmers propel themselves (action - reaction, propulsion from the Bernoulli principle, propulsion from vortices, propulsion from axial flow). In conclusion, it remains unclear which mechanism is most responsible for propulsion in human swimming. However, there is strong evidence that generation of lift by sculling the hand at small angles of attack to generate lift in accordance with the Bernoulli Principle is not the main mechanism of propulsion. Combinations of lift and drag forces, with drag being the more dominant throughout most of the stroke appear likely for front crawl, butterfly, and backstroke. One might expect that the role of lift in breaststroke is more substantial than in the other strokes. There is a growing body of evidence that production and shedding of vortices plays an important role in propulsion. That propulsive force is generated by axial flow in accord with the `pumped up propulsion` hypothesis is an exciting new possibility. Indeed propulsion in swimming could be an interaction of various mechanisms. There may even be others awaiting discovery!