What can the shape and size of a galaxy tell us about how it has evolved across cosmic time? Which evolutionary mechanisms are important, or relevant, and which not? How do galaxies form in the early Universe? As we enter a new era of big-data astronomy, our capacity to further pursue answers to these questions is increasingly limited not by Human ingenuity but by our use of 20th century data analysis techniques. In this talk, I will summarise my work with the Galaxy And Mass Assembly (GAMA) Survey in measuring the multi-wavelength light profile and stellar mass properties of ~200,000 galaxies in the local Universe. I will show how the stellar mass function may be broken down by morphology and structural component, and the implications this has for our understanding on which evolutionary mechanisms are important in shaping the galaxies around us over the course of the last 1 billion years.