This chapter focuses on the properties of moderately and heavily doped silicon (Si) and germanium (Ge); lightly doped crystals are only briefly considered in it. It discusses the work (experimental as well as theoretical) that helps in understanding the physics of bandgap narrowing (BGN) and the effect of BGN on device performance. A historical survey of the work done on BGN is outlined in the chapter, followed by the theoretical work on BGN. The effect of concentration fluctuation and the theory of band tails are also discussed in the chapter, followed by the effect of BGN on optical properties of Si and Ge. In calculating the donor and acceptor impurity states in semiconductors, several approximations have to be made. In many calculations, the band is assumed to be isotropic and parabolic, the electrons and holes are described by effective masses, and the screened Coulomb potentials are used in the Hamiltonian. © 1991, Elsevier Science & Technology. All rights reserved.