Perhaps the most basic defining feature of a galaxy is that its starlight is typically divided between disk and spheroidal components.  From the earliest studies, the way the light was split between these components formed a key element of the way in which galaxies were classified, and this parameter has remained central as techniques have advanced to a point where a galaxy can be quantitatively decomposed into bulge and disk components.  However, a physical interpretation for this division of light has proved difficult to pin down on the basis of such photometric bulge-disk decompositions.  Here, I will present two new methods that take such decompositions to a new level, which allow a more physical understanding of the components.  First, I will present spectral bulge-disk decomposition, which allows us to study the detailed properties of the individual stellar populations in these components, and hence their origins.  Second, I will describe kinematic bulge-disk decomposition, which allows us to use dynamical information as well as spatial data to understand the properties and sources of the components.  Application of these techniques to S0 galaxies finally enables us to reconstruct the life histories of these common systems.