Rotation and internal gravity waves in low-mass stars

We discuss the successes and failures of self-consistent rotating models of main sequence and slightly evolved low-mass stars. We focus in particular on the strongest observational constraints which are the lithium surface abundances and the solar rotation profile deduced from helioseismology. We recall that the hot side of the so-called lithium dip is well explained by hydrodynamical models where the transport of angular momentum is carried out by meridional circulation and shear turbulence. For cooler stars however the transport of angular momentum is dominated by another process. We show that internal gravity waves are the best candidate and we explain how the mass dependence of this mechanism is expected to resolve the enigma of the lithium dip in terms of rotational mixing, forming a coherent picture in main sequence stars of all masses.