These lecture notes review the LDA-KKR-CPA method for treating the electronic structure and energetics of random alloys and the MF-CF and GPM theories of ordering and phase stability built on the LDA- KKR-CPA description of the disordered phase. Section 2 lays out the basic LDA-KKR-CPA theory of random alloys and some applications. Section 3 reviews the progress made in understanding specific ordering phenomena in binary solid solutions base on the MF-CF and GPM theories of ordering and phase stability. Examples are Fermi surface nesting, band filling, off diagonal randomness, charge transfer, size difference or local strain fluctuations, magnetic effects; in each case, an attempt is made to link the ordering and the underlying electronic structure of the disordered phase. Section 4 reviews calculations of electronic structure of {beta}-phase Ni{sub c}Al{sub 1-c} alloys using a version of the LDA-KKR-CPA codes generalized to complex lattices.