In recent years the class of materials known as intermediate valent, Kondolattice or heavy-fermion systems has aroused much interest. The unusual properties of these materials arise from the behaviour of their 4f-(or 5f-)electrons. The strong electron-electron interactions within the 4f shell cause the f-bands of these rare earth or actinide metal containing species to show very high masses. Thus the densities of states are very high, leading to correspondingly high specific heats and magnetic susceptibilities. A mean field theory is described, based on the Anderson lattice model, in which these properties are straightforwardly explained. Its relationship to the 1/N expansion, and the corrections to mean field, are outlined. © Taylor & Francis Group, LLC.