Atomic-scale theoretical investigations of clean and covered low-index surfaces of compound semiconductors are presented. Particular emphasis is laid on the role of the electron counting rule (ECR) in governing plausible surface reconstructions. Trends are presented for the characeristic tilt of the topmost atomic layer and the highest localised phonon mode on nonpolar III-V(1 1 0) surfaces, including III-nitride compounds. Reconstructions and electronic properties of polar surfaces are explained in terms of dimer formation on (0 0 1), and trimer and/or chain formation on (1 1 1) faces. It is pointed out that some surface reconstructions stabilise as a result of a balance between the ECR and minimization of adsorbate-induced local distortion. This is demonstrated for the long-range ordered reconstruction on the Sb:GaAs(1 1 1)B surface. (c) 2004 Elsevier B.V. All rights reserved.