When light is absorbed in matter, electrons are excited to higher levels, leaving empty “hole” levels behind. The electrons and holes can form bound states called excitons, which give rise to prominent features in the optical spectra of insulators and semiconductors. In this talk I will give an introduction and overview to the theory and applications of excitons. We will begin with a simple hydrogen-like model, then go over some modern quantum mechanical approaches of computational materials science. Finally, we will discuss the important role played by excitons in photovoltaics.