Physical and chemical trends of the properties of semiconductors are studied on the basis of first-principles electronic structure calculations. Total-energy calculations for compounds under pressure and in various (hypothetical) crystal structures are performed within the local-density approximation. The self-consistent band structures are calculated by means of the LMTO method. By transformation of the orbitals to an orthogonal basis sp³ bond orders are derived, and a transformation to a tight-binding basis allows the derivation of ionicities, polarities, metallicities etc from the first-principles potential parameters. The theoretical ionicities relate fairly well to the empirical Phillips scale, and it is shown that a critical value close to 0.8 separates the fourfold and sixfold coordinated crystal structures. Optical-phonon and "absolute" hydrostatic deformation potentials are derived, and a simple scheme is suggested for the calculation of band lineups in semiconductor heterostructures. The band offsets are derived from the assumption of a partial alignment of the "dielectric midgap energy" (DME) levels of the two compound semiconductors. The DME is related to the charge-neutrality points introduced by Tejedor and Flores, and by Tersoff.