Atomic layer epitaxy (ALE) has been recently established as a new growth technique which allows control of the growth process at the monolayer level through a self-limiting growth mechanism. We report here on recent progress and current problems facing this technology. Side wall growth by ALE has been demonstrated with deposited structures that differ from conventional chemical vapor deposition growth. Also ALE shows promise in the growth of GaAs on nonpolar substrates such as Ge. The problem of background doping in ALE films will be addressed. © 1988.