Certain marine unicellular cyanobacteria of the genus Synechococcus exhibit a unique type of swimming motility characterized by the absence of flagella and of any other obvious organelle of motility. Although the mechanism responsible for this phenomenon remains mysterious, recent advances have included the development of testable models as well as the identification of a cell-surface polypeptide that is required for the generation of thrust. These developments, as well as the future research directions they suggest, are discussed.