Microtubules are fibrous elements in the cytoplasm of eukaryotic cells, where they perform a wide variety of functions. Microtubules are major organizers of the cell interior and are vitally involved in motility events such as chromosome migration during cell division. To fulfill their physiological function, microtubule arrays have to undergo dramatic changes in their spatial arrangement, and this depends to a large extent on the complex and special dynamic properties of the individual polymers. In this review we first describe the intrinsic dynamic properties of microtubules assembled in vitro from purified tubulin and examine the relationships between these properties and microtubule functions. Subsequent sections concern microtubule dynamics in vivo, their similarity and differences with microtubule dynamics in vitro, and the nature of the cellular regulators which act on microtubule assemblies in physiological conditions.