Current problems in stellar pulsation theory

The last decade lead to major progress in asteroseismology and stellar physics with the advent of space missions. Thanks to the richness and precision of current oscillation spectra, sophisticated seismic probing techniques allow us now to pinpoint the limits of our current models of stellar structure and evolution. However, the accuracy of the seismic diagnosis depends on the accuracy of the pulsation models. In solar-like oscillations, the main source of inaccuracy comes from the near-surface layers where the oscillations are non-adiabatic and strongly coupled with turbulent convection. Some pulsating stars rotate fast and this must be accurately taken into account in the modeling of their pulsations. In others, the magnetic field or the dynamic tides could play some role. I propose here an overview of the great achievements and current limitation of asteroseismology