In this review we first present the two classes of non-reactive and reactive surfactants effective during homoepitaxy and heteroepitaxy, respectively. We then describe and analyse the results obtained by ''true'' surfactant-mediated molecular-beam epitaxy (SM-MBE) of Ga1-xInxAs layers on GaAs substrates. Then, the data obtained by using In as a ''virtual'' surfactant during SM-MBE of InAs layers on AlxGa0.48-x In0.52As/InP and GaAs substrates are presented. We finally provide evidence that the growth mode influences the resulting defect microstructure in (partially) relaxed layers.