In situ studies of the fundamental processes involved in film growth by molecular beam epitaxy (MBE) have reached the point where atomistic models can be developed and compared directly with theoretical predictions. In this paper, we discuss two material systems to illustrate aspects of growth chemistry, adatom incorporation and strain relaxation. We deal first with the homoepitaxial growth of GaAs(0 0 1) from beams of Ga, As 2 and As 4, starting from an historical perspective and then relating the very early work to present day scanning tunnelling microscopy (STM) studies, made in conjunction with kinetic Monte Carlo (KMC) simulations which take account of the actual surface structure. We then demonstrate the uniqueness of (0 0 1) growth in comparison with growth on other low-index orientations. The InAs–GaAs system provides the archetypal illustration of the effects of misfit and we indicate how in situ studies with reflection high-energy electron diffraction (RHEED) and STM have shown that again growth on (0 0 1) oriented substrates is completely different from that observed on (1 1 0) or (1 1 1) orientations in terms of growth mode and strain relaxation behaviour. The formation of quantum dots is not simply strain-related.