  This article first reviews the basic physics of rotating stars and their
evolution. We examine in particular the changes of the mechanical and thermal
equilibrium of rotating stars. An important (predicted and observed) effect is
that rotating stars are hotter at the poles and cooler at the equator. We
briefly discuss the mass loss by stellar winds, which are influenced by the
anisotropic temperature distribution. These anisotropies in the interior are
also driving circulation currents, which transports the chemical elements and
the angular momentum in stars. Internal differential rotation, if present,
creates instabilities and mixing, in particular the shear mixing, the
horizontal turbulence and their interactions. A major check of the model
predictions concerns the changes of the surface abundances, which are modified
by mass loss in the very massive stars and by rotational mixing in O- and
B-type stars. We show that the observations confirm the existence of rotational
mixing, with much larger effects at lower metallicities. We discuss the
predictions of stellar models concerning the evolution of the surface
velocities, the evolutionary tracks in the HR diagram and lifetimes, the
populations of blue, red supergiants and Wolf-Rayet stars, and the progenitors
of type Ibc supernovae. We show, that in many aspects, rotating models provide
a much better fit than non-rotating ones. Using the same physical ingredients
as those which fit the best the observations of stars at near solar
metallicities, we explore the consequences of rotating models for the status of
Be stars, the progenitors of Gamma Ray Bursts, the evolution of Pop III stars
and of very metal poor stars, the early chemical evolution of galaxies, the
origin of the C-enhanced Metal Poor stars (CEMP) and of the chemical anomalies
in globular clusters.
