The stellar population of a galaxy contains a record of its star formation and assembly history and so is an important focus of research for understanding galaxy formation and evolution. We present results from two studies, the first focusing on early-type galaxies (ETGs) and the second on star-forming galaxies (SFGs). These works explore the link between the overall structure and dynamics of galaxies and the evolution of their stellar populations, both before and after galaxies have quenched. The well-established scaling relations between the masses of galaxies and the properties of their stars are generally considered evidence for mass being the principal driver of stellar population evolution. However we show, for both ETGs and SFGs, that the relations between metallicity and gravitational potential and between age and surface density have smaller scatter and less residual trend with galaxy size than the relations of these quantities with mass. The observation that the scaling relations between stellar population and galaxy dynamical structure previously seen in ETGs are also found in SFGs has implications for the types of processes causing quenching and for their timing with respect to star formation and morphological transformation.