Atomic layer epitaxy (ALE) of III-V compounds is addressed, with particular focus on ALE by chloride source gases of group III elements and hybrids of group V elements. A self-limiting growth mechanism in ALE is the most significant advantage over other epitaxial methods. To realize this mechanism, selections of source gases and the reactor gases and the reactor design are described. The chemistry and growth kinetics of ALE, which also provide interesting information for understanding other vapor phase epitaxy (VPE) processes, are discussed, and a model of the self-limiting growth mechanism for chloride ALE is proposed. As a promising application of ALE, the growth of fine structures using sidewall epitaxy and selective area growth is demonstrated. Prospects for the future are briefly discussed.>