Metal-semiconductor, semiconductor-semiconductor and insulator-semiconductor interfaces are basic constituent elements of semiconductor devices. How energy bands align at these interfaces and how well carriers are controlled through these interfaces have been important research topics of surface science as well as basic design issues for semiconductor devices. This paper attempts to review the historical evolution of various models concerning the alignments of energy bands and related Fermi level pinning phenomena at inorganic crystalline semiconductor interfaces, mainly focusing on those of compound semiconductors. The topics discussed include the natural band line-up, surface state model, charge neutrality level, interfacial model, MIGS model, UDM, DIGS model, interface bond polarization model, IFIGS model and model solid theory. It is suggested as a result of reviewing that, by sufficiently removing bond disorder and defects, the natural band line-ups may become realizable after all with feasibility of their artificial modifications by polarization of interface chemical bonds. The strong Fermi level pinning at metal-semiconductor interfaces may be removed in nano-scale structures.