Understanding of the detailed reaction mechanisms during MOVPE and ALE is essential to further improve the properties of the grown crystals and the controllability of the growth parameters. The unified models for the detailed reaction paths are not available at this stage. The study, however, has been advanced to the extent that consensus on some of the reaction paths can be drawn from the scattered data. Metalakyls such as TMGa and TMIn seem to nearly fully decompose in the gas phase through homogeneous reaction at the typical MOVPE growth temperature. Hydrides such as AsH3 and PH3, on the contrary. seem to decompose heterogeneously onthe substrate surfaces as well as homogeneously in the gas phase. However, at lower temperatures, where ALE crystals are typically grown, the growth process is strongly dependent on the surface reactions. It seems that steric hindrance effects which the radicals reaching the substrate exhibit on the surface the growth rate a function of the metalalkyle supply durations. In addition, dydrogens released from hydrides seem to play an essential role in removing carbons leberated from the metalalkyls. High growth temperatures also seem to be effective in desorbing carbons from surface. The understanding of the reaction mechanisms was possible though diverse appraaches utilizing many ex-situ and in-situ diagnostic techniques and genuine experimental designs. It is the purpose of this paper to review and discuss many of these efforts and to draw some possible conclusions from them.