Kinesins are a diverse superfamily of microtubule-based motors that perform fundamental roles in intracellular transport, cytoskeletal dynamics and cell division. These motors share a characteristic motor domain that powers unidirectional motility and force generation along microtubules, and they possess unique tail domains that recruit accessory proteins and facilitate oligomerization, regulation and cargo recognition. The location, direction and timing of kinesin-driven processes are tightly regulated by various cofactors, adaptors, microtubule tracks and microtubule-associated proteins. This Review focuses on recent structural and functional studies that reveal how members of the kinesin superfamily use the energy of ATP hydrolysis to transport cargoes, depolymerize microtubules and regulate microtubule dynamics. I also survey how accessory proteins and post-translational modifications regulate the autoinhibition, cargo binding and motility of some of the best-studied kinesins. Despite much progress, the mechanism and regulation of kinesins are still emerging, and unresolved questions can now be tackled using newly developed approaches in biophysics and structural biology.