We review the construction of Seiberg–Witten curves for a wide class of four-dimensional \(\mathcal N=2\) theories using techniques from superstring theory and M-theory, following the seminal work of Witten (Nucl Phys B 500:3–42, 1997) and the detailed treatment in Gaiotto et al. (Adv Math 234:239–403, 2013). After a brief overview of superstring and M-theory with emphasis on their brane content, we describe the type IIA brane configurations that realize broad families of \(\mathcal N=2\) gauge theories. Their M-theory uplift yields the corresponding Seiberg–Witten curves, providing a powerful framework for constructing these curves systematically. We then introduce the framework of class \(\mathcal S\) theories, drawing on Gaiotto (JHEP 8:034, 2012; Tachikawa, \(N=2\) supersymmetric dynamics for pedestrians, 2013). We first show how the S-duality properties of four-dimensional \(\mathcal N=2\) *** \(\mathrm {SU}(2)\) SYM with four flavors give rise to generalized \(\mathrm {SU}(2)\) quivers, which capture weak-coupling limits of a broad class of \(\mathcal N=2\) superconformal field theories, namely class \(\mathcal S\) theories of type \(A_1\) . This construction naturally generalizes from \(\mathrm {SU}(2)\) to \(\mathrm {SU}(3)\) and, more generally, to \(\mathrm {SU}(N)\) .