The technique of microzone recrystallization from the melt is now well established for InSb following its initial success with Ge, and the key development which has established the art is the use of a containment layer. Providing the zone-scanning rate is slow enough, large nondendritic crystals can be grown and the recrystallized films exhibit similar transport properties to those of bulk material having the same composition, provided the film exceeds a critical thickness dependent upon donor density. Agreement between measured room temperature mobility as a function of thickness and the predictions of the simple model of Many, Goldstein, and Grover confirm that surface scattering in microzone recrystallized films is predominantly diffuse. With the success of microzone recrystallization, the problem of producing films with high electron mobility has changed from that of growing large crystallites to that of obtaining a composition close to a stoichiometric and a low donor density. Microzone recrystallization from the melt should be extendable to other IIIA-VA compounds. It should also be possible to exploit the microzone in the growth of crystals by techniques other than growth from the melt. This is particularly applicable to IIB-VIA compounds and some preliminary evidence suggests that recrystallization of CdS films can be achieved in this way.