"Excitons" are exciting objects. In the simplest setting, the notion of an exciton refers - roughly - to spacially localized, generally time dependent deviations of the state of a multi-electron system from its ground state. Thus, an exciton corresponds to the solution of a many-body quantum-mechanical problem. Yet, excitons are often synonymously referred to as "electron-hole pairs", suggesting that their dynamics can be described effectively as that of two interacting quasi-particles. In this seminar, we will study some of the cornerstone publications on the theory of excitons, including, e.g., groundbreaking work by Frenkel (strongly localized excitons, typically found in organic semi-conductors), Wannier and Mott (more distributed excitations in the form of WKB-type wavepackets), Hedin (a fundamental attempt to connect the theory to the many-body electronic problem via Green's functions), Bethe & Salpeter (many-body perturbation theory building strongly upon Hedin's work), or the much more recent work by Cancès and co-workers who are working today on the rigorous mathematical formalization and justification of these theories from the physical sciences.