Actin filaments and microtubules form the cytoskeleton of all eukaryotic cells, and they are responsible for organizing the cytoplasm and supporting motile processes. Both polymers are highly dynamic, and their polymerization dynamics are central to their organization. Though their evolutionary origins appear to be distinct, actin and tubulin have a similar mechanism for promoting polymerization dynamics in which the energy of nucleotide triphosphate hydrolysis during polymerization is used to weaken the bonds between subunits, thus promoting subsequent depolymerization. The evolutionary origins of actin and tubulin are unclear. It is likely that motile mechanisms driven by reversible polymerization, termed thermal ratchets, are older than those based on ATPase motor proteins. Such mechanisms are still important in modern eukaryotes, and may have powered early versions of the critical motile processes of phagocytosis and chromosome segregation in primitive cells. Thus evolution of dynamic cytoskeletal polymers may have been one of the earliest and most important steps leading to the evolution of eukaryotes. Plausible evolutionary pathways can be constructed leading from simple enzymes to dynamic cytoskeletal polymers.