The population of massive galaxies in the local Universe is dominated by quiescent, spheroidal systems. This population has grown in number and mass density over the last 8-10 Gyr, at the expense of the star-forming population. The evolution with redshift of galaxies stellar populations in relation to galaxy mass, structure and kinematics can constrain the past star formation history and galaxies evolutionary path. With these goals, the LEGA-C public spectroscopic survey has just finished collecting high-S/N rest-frame optical spectra of a K-band selected sample of ~3000 quiescent and star-forming galaxies at redshift 0.6