The article presents a short review of recent developments in epitaxial lateral overgrowth (ELO) of thin layers of III-V compound semiconductors by liquid phase epitaxy (LPE) and also by liquid phase electroepitaxy (LPEE). The focus is on the relative contributions of various transport processes involved in ELO toward the growth of high quality, dislocation free thin layers of semiconductors with large width/thickness ratios. Results of our experimental and modelling studies on lateral overgrowth by LPE are used as examples. Furthermore, the application of LPEE for lateral overgrowth of compound semiconductors, a new emerging area of ELO technology, is discussed, and some experimental and numerical results are presented.