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Variable stars with the Kepler space telescope

The Kepler space telescope has revolutionised our knowledge about exoplanets and stars and is continuing to do so in the K2 mission. The exquisite photometric precision, together with the long, uninterrupted observations opened up a new way to investigate the structure and evolution of stars. Asteroseismology, the study of stellar oscillations, allowed us to investigate solar-like stars and to peer into the insides of red giants and massive stars. But many discoveries have been made about classical variable stars too, ranging from pulsators like Cepheids and RR Lyraes to eclipsing binary stars and cataclysmic variables, and even supernovae. In this review, which is far from an exhaustive summary of all results obtained with Kepler, we collected some of the most interesting discoveries, and ponder on the role for amateur observers in this golden era of stellar astrophysics.