Band theory forms the foundation for understanding the electronic properties of solids. In the beginning, this chapter presents the historical aspects of early models of metals and traces the development of free-electron, nearly free-electron, and tight-binding theories. Various ab initio methods—such as the cellular method, augmented plane wave method, orthogonalized plane wave method, pseudopotential method, Green’s function method, and Korringa-Kohn-Rostoker method—are discussed in relation to evaluating band structures. The history of the experimental determination of Fermi surface using different methods and its construction from the energy bands is presented. The development of density functional theory (DFT) by Hohenberg and Kohn and its applications in calculating electron density and self-consistent potential are covered. In addition to this the development and applications of partial wave method, dielectric screening method, Thomas–Fermi theory etc. have also been described. This chapter also examines the electronic properties such as electrical resistivity, and electric field gradients of concentrated and dilute alloys. Different methods for evaluating the effect of impurity-induced lattice strain on the electronic properties have been pointed out.