The space-borne observatories CoRoT (Convection Rotation and planetary Transits) and Kepler have provided photometric time series data of unprecedented precision for large numbers of stars. These data have revolutionized the fields of transiting exoplanets and asteroseismology. In this review some important asteroseismic results obtained using data from the CoRoT and Kepler space missions concerning stars that show solar-like oscillations are discussed. These results comprise, among others, measurements of the location of the base of the convection zone and helium second-ionization zone in main-sequence stars, the presence (or not) of core-helium burning in red-giant stars, as well as differential rotation in these stars.