After a general introduction into the research field of asteroseismology, we review the highlights achieved from multi-site ground-based campaigns dedicated to carefully selected targets. We show how asteroseismology has the potential to improve stellar evolution models to a level that cannot be achieved by any other method so far. Subsequently, we discuss several results from the operational French-led European space mission CoRoT (Convection, Rotation, planetary Transits) for various types of stars and illustrate the immense advantage of having long-term uninterrupted data from space with a factor 100 better precision compared to data from the ground. Finally, we will highlight the next step expected in this research, based on data assembled by the space mission Kepler (NASA) which has been designed primarily for exoplanet hunting. This mission, along with the future ESA PLATO satellite project, will allow us to do asteroseismology of numerous exoplanet host stars.