It is shown that the existence of superconductivity in a material, and its critical temperature, depends strongly on pressure. Several parameters are pressuredependent: (1) structure, particularly bond distances, (2) Hubbard U , (3) coupling between sites, and (4) orbital occupation number. Eliashberg theory often leads to incorrect predictions, for example in A 3 C 60 with A = K, Rb, and Cs. While T C is correctly predicted to be higher for Rb 3 C 60 than for K 3 C 60 and decreasing with pressure in both cases, Cs 3 C 60 is not superconducting at ambient pressure. The same is the case for pure metals such as Cs and Ca (superconducting at high pressure). A theory for electron pairs, similar to the Marcus model for single electrons, appears to agree with the experiment in most cases.