The CdTe and CdZnTe growth are reviewed. After presenting briefly the most recent results concerning the phase equilibria in the Cd-Te system, the impact of the characteristics of the Cd-Te chemical bond on the CdTe crystal growth are discussed. The behaviour of Zn alloying in CdTe is then presented at macroscopic and microscopic scale. Furthermore, the strains introduced by the Zn segregation in the alloys are estimated and shown close to the CZT CRSS. Some improvements in the CZT growth are finally presented and discussed: the adjustment of the CZT stoichiometry, the Zn concentration uniformity issue and the strain issue in the alloys which can be overcome by microgravity growth, self-seeding from a free liquid surface, solid state recrystallization and/or dewetting.1I ntroduction CdTe has attracted great interest and found several industrial applications since now forty years. It shows unique properties making it important and very suitable for several applications like photovoltaic conversion, nuclear detection, application for which it has a tremendous potential, mainly for medical purposes, high performance electro-optic modulators and photorefractive devices. It presents both types of conductivity making diode technology and field effect transistors possible. CdTe-based semimagnetics, like CdMnTe, display extremely exciting properties which have not been so far completely exploited. Furthermore, CdZnTe is used as a substrate for the epitaxial deposition of HgCdTe layers.In view of all these applications, considerable efforts have been dedicated since more than forty years to the crystal growth of CdTe which will be reviewed in close relationship with its intrinsic properties, mainly those that come directly from the characteristics of the Cd-Te chemical bond.2P hase equilibria in the Cd-Te system Crystal growth of CdTe requires precise knowledge of the existence regions of the solid, liquid and gas phases with respect to temperature, pressure and composition. For this purpose, the temperature versus composition, T-x , component pressure or total pressure versus temperature, p-T or P-T, and finally p-T-x or P-T-x diagrams have been experimentally determined and theoretically modeled. In order to control the stoichiometry of the crystals, the deviations from which affect strongly their semiconducting properties, the knowledge of the extent of the homogeneity domain and of the position of the stoichiometric line inside the three phase boundary is essential as well.After many experimental investigations and theoretical studies [1], the Cd-Te phase diagram has been revisited from total vapor pressure scanning experiments by J.H. Greenberg [2]. The determination of the *