The cross sections of certain nuclear reactions, as functions of energy, show sharp maxima and low values between the maxima, thus exhibiting a great similarity to line spectra. The compound nucleus theory was originally designed to explain this structure and to describe the corresponding nuclear reactions. After a brief description of the picture which the compound nucleus theory presents for these reactions, the story of the extension of the theory to describe a wide variety of reactions is presented. This includes an outline of the mathematical concepts which the extended theory uses. The last part of the article deals with the connection between the so-called principle of causality, which expresses the fact that the scattered particle wave cannot leave the nucleus before the incident particle wave has reached it, and the formulas of the generalized compound nucleus theory.