The fundamental growth issues of AlN and AlGaN on sapphire and SiC using metalorganic vapor phase epitaxy, particularly the growth of AlN and AlGaN on a groove-patterned template are reviewed. In addition, the conductivity control of AlGaN is shown. The conductivity control of p-type AlGaN, particularly the realization of a high hole concentration, is essential for realizing high-efficiency UV and DUV LEDs and LDs.