The chemistry of oxide superconductors, especially those of the YBa//2Cu//3O//x family, is discussed with respect to their crystal growth. YBa//2Cu//3O//x melts incongruently, loses oxygen at elevated temperatures and reacts with water. Present knowledge of the appropriate phase diagrams is reviewed. Major important methods of crystal growth are summarized and their present applicability to YBa//2Cu//3O//x is discussed. In addition, recent results on the melt growth of bulk crystals from melt compositions near the ternary eutectic and on the growth of thin oriented, partly epitaxial films by vapor growth using thermal and e-beam vapors and MBE are described.