Mechanical work in cells is performed by specialized motor proteins that operate in a continuous mechanochemical cycle. Less complex, but still efficient, ‘one-shot’ motors evolved based on the assembly and disassembly of polymers. We review the mechanisms of pushing and pulling by actin and microtubule filaments and the organizational principles of actin networks. We show how these polymer force generators are used for the propulsion of intracellular pathogens, protrusion of lamellipodia and mitotic movements. We discuss several examples of cellular forces generated by the assembly and disassembly of polymer gels.