Growth of binary and ternary single crystals which have complete miscibility in the phase diagrams, have been studied by several newly developed methods such as the liquid encapsulated Czochralski, Bridgman, and multi-component zone melting methods for InGaAs bulk crystals, and the multi-component zone melting methods and Bridgman methods for Ge-rich and Si-rich SiGe bulk crystals. Crystals grown by these methods are compared with each other, to find the proper growth conditions to obtain single crystals with uniform composition. Techniques for the precise control of the temperature at the growing interface and for the continuous supply of the depleted solute elements to the growth melt were developed. InGaAs bulk crystals with uniform composition were obtained by the multicomponent zone melting method. Si-rich and Ge-rich SiGe bulk crystals with uniform composition were obtained in the Ge compositional range from 10 to 78%. The advanced technologies to obtain the InGaAs and SiGe bulk crystals with much higher-quality are discussed in this paper.