Deriving the azimuthally averaged radial surface brightness profile of a galaxy is a schematic way of presenting the light and then the mass structure of disc galaxies. In this overview we will dwell on the outer discs, as it has become possible, with modern data to explore the light profile out to ever increasing galactocentric radii. We find that these profiles can be well classified into three main types: truncated profiles, untruncated profiles, and antitruncated profiles, denoted as Types II, I, and III, respectively, amplifying an original classification into Types I and II by Freeman. We present statistics of these types over the range of the Hubble galaxy classification for 187 nearby galaxies. We then analyse a sample of disc profiles for a sample of nearly 500 galaxies in three redshift bins, out to z = 1.1, from HST data. For the Type II discs we show that the “break” radii where the inner disc slope changes to a more abrupt outer slope have increased with epoch, but that at all epochs this radius has the bluest, i.e. the youngest stellar population. This can be explained via models which combine stellar migration due to non-axisymmetry with continuous star formation due to gas infall, one version of inside-out disc growth. We note that the observed features of Type I and Type III profiles are not explained in this scenario and show the need for even deeper profiles, especially in the IR, the UV, and Hα.