Semiconductor behaviour was predicted and discovered in the III-V semiconductor compounds almost 50 years ago at the beginning of the 50s. The demand for high-purity single crystals was axiomatic in view of the prior pioneering research on germanium as a semiconductor device material. However, while the development of semiconductor grade Ge took about a decade, the comparable development of the readily dissociable Ill-V compounds have followed a very much slower evolution, which is still in progress. This review discusses some of their intrinsic material problems and some of the solutions that have required so much research and development effort to produce single crystal compounds suitable for high-performance devices. The primary focus of the paper is the compounds of major commercial importance, GaAs and InP. While most of the problems that arise in the growth of high-quality single crystals of these materials have been endured over the years, new and more refined technical and scientific solutions to these have been developed. The growth techniques that will be considered include Liquid Encapsulation, Vertical Gradient Freeze, Vapour Pressure Controlled Czochralski and Hot Wall Putting techniques including Pressure Balancing. The practical constraints to implementing these techniques and their advantages and limitations are considered. Problems of twinning, cellular structure, dislocation formation, lineage, constitutional supercooling and defects are reviewed. The significance of technique in relation to recent developments in commercial exploitation, especially with regard to size, is noted. In addition, related areas of scientific interest which have either not been researched significantly or could be of future significance such as the potential of electromagnetic stirring are highlighted. (C) 2004 Elsevier B.V. All rights reserved.