In this talk I will review the emergence of Yang-Mills theories and other related gauge theories (including Seiberg-Witten theories and Hitchin Systems) as they arise in modern string theory constructions. I will demonstrate the way that string dualities can relate seemingly disparate geometric systems and shed light on novel underlying mathematical structure. As one example, I will focus on generalizations of Hitchin systems and Higgs bundles as they appear in compactifications of F-theory.