The best way to trace back the history of star formation and mass assembly of the Milky Way disc is by combining chemical compositions, ages and phase-space information for a large number of disc stars. With the advent of large surveys of the stellar populations of the Galaxy, such data have become available and can be used to pose constraints on sophisticated models of galaxy formation. We use SDSS-III/APOGEE data to derive the first detailed 3D map of stellar density in the Galactic disc as a function of age, [Fe/H] and [α/Fe]. We discuss the implications of our results for the formation and evolution of the disc, presenting new constraints on the disc structural parameters, stellar radial migration and disc flaring. We also discuss how our results constrain the inside out formation of the disc, and determine the surface-mass density contributions at the solar radius for mono-age, mono-[Fe/H] populations.