We demonstrate the use of density-functional theory (DFT) calculations for understanding molecular beam epitaxy (MBE) of GaAs and InGaAs films at the atomic level. For analyzing island growth in homoepitaxy of GaAs(0 0 1), the use of DFT in conjunction with kinetic Monte Carlo (kMC) simulations is discussed. This approach enables us to elucidate the growth mechanisms of islands on the beta2(2 x 4)-reconstructed surface and to compute the saturation values of the island density. Furthermore, DFT calculations are employed to investigate the stability of ultrathin InGaAs films on GaAs(0 0 1) as a function both of the chemical potential of arsenic in the growth environment, and of mechanical strain. Under very As-rich conditions, for deposition of two-thirds of a monolayer (ML) of InAs, our calculations indicate the formation of a (2 x 3)-reconstructed InGaAs(0 0 1) surface alloy. The calculated atomic structure is in excellent agreement with X-ray diffraction data. For less As-rich conditions and larger amounts of deposited InAs, we find InGaAs films with a alpha2(2 x 4) reconstruction to be most favorable. (C) 2003 Elsevier Science B.V. All rights reserved.