The recent space age of uninterrupted high-precision photometry finally offered us a way to look deep inside stars. This deep probing is possible thanks to the detection of numerous stellar oscillations. The observed properties of such oscillations allow us to derive how stars age, how they rotate, and how they mix their gas throughout their life. In this Colloquium, we start with the basic ingredients of asteroseismology for the non-expert. We discuss the diversity of nonradial oscillations of stars, introducing pressure, gravity, magnetic, and tidal waves. We then emphasize some of the breakthroughs from space asteroseismology, focusing mostly on results from the 4-year Kepler light curves. Examples involve high-precision sizing, weighing, and ageing of stars throughout our Milky Way. We review the current status of the internal rotation of stars and offer a sneak-preview on internal mixing inside stars with a convective core as new observational input to calibrate stellar evolution theory. We end with a future outlook for this glorious research field of astrophysics, touching upon how to achieve probing of internal magnetism and tidal asteroseismology, thanks to the ongoing NASA TESS and future ESA PLATO space missions.