Metal organic vapour phase epitaxy (MOVPE) is nowadays one of the leading techniques for epitaxial growth. While the processes in the gas phase of MOVPE are reasonably well understood, the processes on the growing surface are not. This situation is in contrast to molecular beam epitaxy (MBE), where considerable knowledge about growth processes on the surface could be gained. The main reason is that all the UHV-based classical surface-science tools (using electrons and ions), especially reflection high-energy electron diffraction, can be applied in the vacuum-based MBE but not under the gas-phase conditions of MOVPE. This situation has changed in the last decade since optical surface-science tools have been developed. Especially, with the linear optical techniques like reflectance anisotropy spectroscopy and spectroscopic ellipsometry, there is now a quasi-standard tool at hand which allows for the study of all kinds of pregrowth and growth situations in MOVPE (in MBE of course, as well). These optical methods give, moreover, chemical information also. In this article we will describe shortly the features of these optical techniques and then concentrate on III-V-semiconductor growth. The spectral definition of surface reconstructions and time-resolved studies of phase transitions between them (adsorption/desorption kinetics of group-III and group-V elements) are discussed next. Under growth, the surfaces can be classified and defined according to their optical surface response into a pressure versus temperature phase diagram. The regions of such a phase diagram correspond to different geometrical and chemical surface structures and consequently lead to different growth modes. Finally, as an example of modern nanogrowth, monitoring of the growth of quantum-dot structures is presented.