The geometric Langlands program arose in the 1980's as an analogue of the Langlands program for algebraic curves, but only recently were Arinkin and Gaitsgory (2012) able to formulate a plausible categorical version of the conjecture. A few years earlier, Kapustin and Witten (2006) placed a version of the categorical conjecture in a physical context, but their work didn't capture the algebro-geometric nature of the conjecture nor did it address the subtleties Arinkin and Gaitsgory had to overcome. After setting up a rigorous mathematical model for Kapustin and Witten's theory, we identify the physics of the Arinkin-Gaitsgory formulation of the conjecture. Moreover, from the physical interpretation, we suggest some curious factorization structure in the geometric Langlands theory. This is based on a joint work with Chris Elliott.