The heavy metals and their intermetallic compounds exhibit a large number of interesting but not well understood properties. This is especially true of the actinides for which little is known about their band structures with which to interpret their observed magnetic, optical and electric properties. This paper describes recent work on these heavy metals (Th through Bk) and some intermetallic compounds of the rare-earths (LaSn3 and LaIn3) and the understanding derived from band theory of the mechanisms responsible for various observed phenomena. Relativistic effects are found to be indispensable for obtaining the correct band structure of the actinide metals. While the 5 f electrons in the lower actinides may be described as band (or itinerant) states, the higher actinides show a marked increase of the localization of the 5 f orbitals and the band description is no longer applicable for these states. Particular attention is paid to the various complications which are faced in determining the band structures of these systems and some of the techniques used in obtaining solutions. Among these are the (obvious) necessity of including relativistic effects, the convergence problems due to the presence of the higher angular momentum states and lowered symmetry, the large number of bands present, the uncertainty in the electronic configuration, and the role of the muffin-tin approximation