Research into dolphin swimming has historically been guided by false assumptions of ‘effortless’, ‘high-speed’ swimming. These assumptions have instigated the development of drag-reduction hypotheses but tests of these hypotheses have generally had little success. The autecological approach has dominated recent efforts and has been more successful. In this review we summarize results of decades of research efforts to study these creatures. (1) Drag is minimized primarily by the streamlined shape of the body and appendages, with no known contributions from compliant dampening, dermal ridges, secretions, boundary layer heating, or skin folds. All indications are that the boundary layer is turbulent. (2) Muscles for the upstroke and downstroke of swimming dolphins provide approximately equal power. (3) Output force is enhanced by insertions occurring on the long processes of the vertebrae and on the subdermal connective tissue sheath. (4) Measured swimming speeds are lower than previously believed, with maximum reported routine speeds being approximately 3 m/s. (5) Porpoising behaviour appears to be the most energetically conservative manner in which to breathe when swimming at high speed. (6) Riding surf and wind waves involves the balance between the wave slope and the weight of the animal whereas riding the bow wave involves the interaction of the pressure wave in front of a ship and the drag of the dolphin.