The chemistry of oxide superconductors, especially those of the YBa2Cu3Ox family, is discussed with respect to their crystal growth. YBa2Cu3Ox 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 YBa2Cu3Ox 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.