Understanding how galaxies obtain baryons, their stars and gas, over cosmic time is traditionally approached in two different ways - theoretically and observationally. In general, observational approaches to galaxy formation include measuring basic galaxy properties, such as luminosities, stellar masses, rotation speeds, star formation rates and how these features evolve through time. Theoretically, cosmologically based models collate the physical effects driving galaxy assembly - mergers of galaxies, accretion of gas, star formation, and feedback, amongst others, to form predictions which are matched to galaxy observables. An alternative approach is to examine directly, in an observational way, the processes driving galaxy assembly, including the effects of feedback. This is a new ‘third way’ towards understanding how galaxies are forming from gas accretion and mergers, and directly probes these effects instead of relying on simulations designed to reproduce observations. This empirical approach towards understanding galaxy formation, including the acquisition history of baryons, displays some significant differences with the latest galaxy formation models, in addition to directly demonstrating the mechanisms by which galaxies form most of their baryonic mass.