Echoing the repeated convergent evolution of flight and vision in large eukaryotes, propulsive swimming motility has evolved independently in microbes in each of the three domains of life. Filamentous appendages – archaella in Archaea, flagella in Bacteria and cilia in Eukaryotes – wave, whip or rotate to propel microbes, overcoming diffusion and enabling colonization of new environments. The implementations of the three propulsive nanomachines are distinct, however: archaella and flagella rotate, while cilia beat or wave; flagella and cilia assemble at their tips, while archaella assemble at their base; archaella and cilia use ATP for motility, while flagella use ion-motive force. These underlying differences reflect the tinkering required to evolve a molecular machine, in which pre-existing machines in the appropriate contexts were iteratively co-opted for new functions and whose origins are reflected in their resultant mechanisms. Contemporary homologies suggest that archaella evolved from a non-rotary pilus, flagella from a non-rotary appendage or secretion system, and cilia from a passive sensory structure. Here, we review the structure, assembly, mechanism and homologies of the three distinct solutions as a foundation to better understand how propulsive nanomachines evolved three times independently and to highlight principles of molecular evolution.