It is notoriously difficult to measure how the interior of stars rotate. So far, this has hindered our progress in stellar modeling because rotation is expected to play a central role in the evolution of stars. The inversion of the internal rotation profile of the Sun obtained from helioseismology in the 90's has revolutionized the field and shown that an efficient and yet unknown mechanism that transports angular momentum operates in the Sun. The space missions CoRoT and Kepler, launched in 2006 and 2009 respectively, have finally made it possible to probe the internal rotation of stars other than the Sun using seismology. In this review talk, we give an overview of the results that were obtained so far, which cover an ever growing part of the HR diagram, from the main sequence (inversions of the rotation profile are starting to be obtained for A, F, and B-type hybrid pulsators) to subdwarf B stars and white dwarfs. A special attention will be given to red giants, in which the detection of so-called mixed modes has made it possible to measure the core rotation rate in several hundreds of targets and to quantify radial differential rotation from the subgiant phase to the core-helium burning phase. These exciting results are giving new momentum to theoretical works tackling the question of angular momentum transport in stars by providing unprecedented observational constraints. We briefly discuss the results of some of the latest studies.

Since the detection of non-radial oscillations in over 10,000 red giants by space missions CoRoT and Kepler, the seismology of these objects has rightfully gained interest among the stellar physics community. The detection of mixed gravity-pressure modes has indeed made it possible to peer into the cores of red giants. This is currently bringing stringent constraints on several physical processes in stellar interiors that remain poorly understood but play a central role in stellar evolution, such as the nature and efficiency of mixing beyond boundaries of convective regions, or the way angular momentum is transported inside stars. We here give an overview of what the seismology of red giants has already taught us about such processes, and highlight the potential of dipole mixed modes in red giants for new advances in stellar physics.