The aim of this thesis is to extend the success of a novel strategy for the interpretation of symmetry-related models — sophistication — to contemporary physical theories’ internal symmetries. In order to do so, I propose that a theory’s quantities possess a certain structure. The problematic underdetermination of symmetry-related models arises when we attribute too much structure to the fundamental quantities. The advantage of sophistication is that it enables a realist interpretation of symmetry-variant quantities, which often figure in the scientific explanation of physical effects. I illustrate sophistication with two case studies: one of mass in Newtonian Gravitation and one of gauge quantities in the Aharonov-Bohm effect. On the trad...