A review is given of III-V epitaxial layer growth by chemical beam epitaxy (CBE), molecular beam epitaxy (MBE) and metal organic vapor-phase epitaxy (MOVPE). The static surfaces of the (0 0 1) facet are reviewed first, after which adatom diffusion during growth on (0 0 1) and (1 1 1) surfaces is discussed. The topic of carrier gas flow and gas phase chemistry as applies to VPE processes is briefly treated next. Finally, chemical reactions are surveyed.