The standard model of stellar structure is unable to account for various observational facts, such as anomalies in the surface composition, and there is now a broad consensus that some extra mixing must occur in the radiation zones, in addition to the always present convective overshoot or penetration. The search for the causes of this extra mixing started in the late seventies, and it was quickly realized – in particular by Sylvie Vauclair and her co-workers – that some mild turbulence must be present to counteract the effect of gravitational settling and radiative levitation. What could be responsible for this turbulence? One suggestion was the internal gravity waves emitted at the boundary of convection zones, but it is still not established whether these waves will lead to true mixing. However they transport angular momentum, and therefore they generate differential rotation, which may be shear-unstable and thus lead to turbulence. Another way to transport angular momentum and produce an unstable rotation profile is through the large-scale circulation which is induced by the structural adjustments as the star evolves, or by the torques applied to it (due to stellar wind, accretion, tides). These processes participate in what is called the “rotational mixing”; their implementation in stellar evolution codes – again under Sylvie's impulse – has given birth to a new generation of stellar models, which agree much better with the observational constraints, although there is still room for improvement.