In this lecture I will review the current theoretical understanding of the production of photons and leptons in ultrarelativistic heavy-ion collisions. Since these electromagnetic probes do not participate in the strong interaction the hot and/or dense medium created in heavy-ion collisions from the lowest to the highest beam energies is transparent for them during the entire evolution of the collision. The invariant-mass spectrum of dileptons as well as the transverse-momentum spectra of dileptons and photons thus provide valuable information about the constituents of hot and/or dense strongly interacting matter, particularly medium modifications of the electromagnetic current-current correlation function and thus sheds light on the question of mass generation of hadrons and the (chiral) phase structure of hot and dense matter. For a realistic theoretical understanding thus one needs both a detailed model for the strong interactions within a hot and dense medium with partonic as well as hadronic effective degrees of freedom, providing the medium modifications of the current-correlation function, and a description of the dynamics of the medium created in heavy-ion collisions to be able to evaluate the dilepton and photon production in heavy-ion collisions and compare them to experiment.
