Islanding and misfit relaxation are obstacles for MBE growth of high quality strained heteroepitaxial layers of lattice-mismatched materials. The growth mode in MBE, and thus the relaxation mechanism of such materials, is determined by balance between free energies of the substrate surface, the epilayer surface, and the interface. In order to reduce epilayer surface and interface free energies in comparison to substrate surface free energy, and thus suppress the process of island formation, use of segregating surface-active species (surfactants) during the MBE growth was proposed already in 1989. The pioneering work of Copel et al. on this subject has been followed by many experimental and theoretical works by other authors. The fundamentals of strained-layer MBE, as well as the most important physical arguments for using surfactants in MBE, are presented and discussed in the first part of this paper. The second part presents experimental examples of advantages resulting from using surfactants and, so called, virtual surfactants in MBE growth of strained heteroepitaxial structures of IV- IV and III-V semiconducting compounds.