This paper reviews the requirements and current practices in the molecular-beam epitaxial (MBE) growth of high-quality GaAs. High-quality growth of GaAs means excellent control on the growth process leading to an excellent surface morphology, structural, electrical and optical properties of the deposited GaAs. Background material is presented about the MBE technique, the MBE system and its initial preparation for growth, molecular-beam source materials, substrate preparation and the growth conditions. The importance of meticulousness at every step is emphasized. Then, to illustrate that the MBE-GaAs has reached a level of perfection, experimental data are presented which show an excellent control on the growth rate and its lateral uniformity (±0.75%), the presence of very low level of background impurities (∼ low 10 13 cm -3) and high electron mobilities (μ peak ∼ 3 × 10 5 cm 2 V -1 s -1 at 42 K for n ∼ 3 × 10 13 cm -3). In addition, it is shown that MBE-GaAs is intrinsically free from electron and hole deep traps. Chemical impurities in the impure arsenic-source are shown to be the main limiting factors in determining the transport and optical properties and formation of deep centers in MBE-GaAs. Such chemical impurities may, however, originate from other sources as well.