Growth of single crystals of the intermediate oxides of titanium, important because of the unique electrical and magnetic properties of these materials, is difficult to achieve in a controlled manner. The difficulties arise for several reasons: the large number of phases in the TiO system, their defect structure and potential for both equilibrium and nonequilibrium disorder of the defects and the change of the oxygen fugacity of the co-existing equilibrium vapor phase with temperature. Precise phase equilibria including solid-vapor equilibria are required and these were first determined in detail.Once these are known several common techniques can be applied to the crystal growth. Reduced rutile has been grown by flame fusion methods for years. We have grown fully oxidized TiO2 at a much lower temperature in hydrothermal highly acidic environments. The higher titanium oxides - TiO2O3, Ti3O3, and the Magneli phases from Ti4O7 to Ti10O19 have been grown from borate fluxes by precise control of the oxygen fugacity in the furnace atmosphere. Extensive characterization of the oxides indicates an unexplored region of possible ordered Magneli phases between Ti10O19 and approximately Ti100O199. Growth of these phases from fluxes with ultra-precise temperature and atmosphere control does not seem impossible.The lower titanium oxides cannot be grown in open systems because of the extremely low oxygen fugacities. The arc-fusion technique of T. B. Reed has proved the best method for preparing high TiO and other phases stable at the melting point. Low TiO remains a crystal-growth problem, as do the oxygen-rich titanium metal phases.