We investigate electric-magnetic duality in Maxwell theory, beginning with vanishing theta angle \(\Theta \) and extending to arbitrary values. Monopoles and dyons can be constructed as solitonic configurations of the Georgi–Glashow model, following the constructions of ’t Hooft–Polyakov and Julia–Zee. Their masses are bounded from below by the Bogomol’nyi bound, which can saturate in the Bogomol’nyi–Prasad–Sommerfield (BPS) limit, giving rise to the notion of BPS states. These ideas extend naturally to non-abelian Yang–Mills theories, leading to Montonen–Olive duality and its connection to Langlands dual Lie groups. Yet, the strongly coupled regime of pure Yang–Mills theory remains elusive, and renormalization further complicates the quantum formulation of duality. \(\mathcal N=2\) supersymmetry substantially refines the study of electric-magnetic duality by granting BPS states remarkable stability properties, thereby providing a window into strongly coupled gauge dynamics. In four dimensions, \(\mathcal N=4\) super-Yang–Mills (SYM) theory is both superconformal and scale-invariant, features that render the conjectural Montonen–Olive duality—referred to as S-duality in that context—particularly natural. Extending S-duality to \(\mathcal N=2\) theories, which encompass a broader and more intricate class of quantum field theories, has yielded significant insights, albeit with considerably greater technical challenges than in the \(\mathcal N=4\) case.