Microtubules are important for organizing and directing many types of intracellular motility. Recently progress has been made in the analysis of two types of motility at the molecular level: the movement of axonal vesicles driven by kinesin, and the movement of chromosomes driven by the kinetochore. Both require ATP for movement in vitro. Kinesin-driven movement is unidirectional, towards the microtubule plus end, while movement of the kinetochore is bidirectional. These similarities and differences are discussed and incorporated into a new model for the kinetochore-microtubule interface.