In this paper, we review recent progress in the theory of non-radiative decay processes in polyatomic molecules. This review has been subdivided into the following sections: I. Introduction II. Brief comments on compound states III. Intramolecular coupling IV. Molecular eigenstates V. Diffuseness and interference effects in the electron spectra of large molecules VI. Intramolecular non-radiative decay VII. Irreversible intramolecular decay in the statistical limit VIII. The coupling between radiative and non-radiative processes in large molecules IX. Conclusions.