A physical picture of molecular beam epitaxy (MBE) growth is presented in a consistent form taking into consideration the atomistic nature of crystallization phenomena occurring in this process. To this end, the entire MBE growth system directly involved in epitaxial crystallization is divided into three different parts. The crystalline solid phase of the substrate, or the already grown epilayer, is one extreme, the gaseous phase of the intersecting molecular beams is the second extreme and the transition layer in between, where transition from a gas to a crystal occurs, creates the third part of the system. The transition layer, where all processes leading to epitaxy occur, is obviously the most important part of the growth system. Its geometrical form and the processes occurring there depend strongly on the growth conditions chosen. The following approaches have been considered when discussing the attributes of MBE growth processes : (i) thermodynamics, (ii) "surface sites-particle" interaction analysis, and (iii) chemical bond quantum mechanics. Taking as examples : (i) MBE of non-stoichiometric structures, (ii) UHV atomic layer epitaxy, and (iii) self-organization effects in MBE, the importance of the transition layer concept for understanding MBE growth processes has been illustrated.