Polymerization and depolymerization of actin filaments and microtubules are thought to generate force for movement in various kinds of cell motility, ranging from lamellipodial protrusion to chromosome segregation. This article reviews the thermodynamic and physical theories of how a nonequilibrium polymerization reaction can be used to transduce chemical energy into mechanical energy, and summarizes the evidence suggesting that actin polymerization produces motile force in several biological systems.