Abstract
One of the most important energy loss mechanisms for very slow electrons travelling through molecular gases is the excitation of rotational states and, less frequently, of vibrational states of the ambient molecules. In this short review the main theoretical aspects of the problem are discussed and the computational methods which have recently produced very good accord with the existing, accurate measurements are presented. The important role played by low-energy, open-channel shape resonances in enhancing the energy transfer mechanism is underlined and shown with computational examples for the polyatomic methane molecule.