Metal-organic vapor phase epitaxy (MOVPE) and molecular beam epitaxy (MBE) are the principal techniques for the growth and n-type (Si) and p-type (Mg) doping of III-nitride thin films on sapphire and silicon carbide substrates as well as previously grown GaN films. Lateral and pendeoepitaxy via MOVPE reduce significantly the dislocation density and residual strain in GaN and AlGaN films. However tilt and coalescence boundaries are produced in the laterally growing material. Very high electron mobilities in the nitrides have been realized in radio-frequency plasma-assisted MBE GaN films and in two-dimensional electron gases in the AlGaN/GaN system grown on MOVPE-derived GaN substrates at the crossover from the intermediate growth regime to the droplet regime. State-of-the-art Mg doping profiles and transport properties have been achieved in MBE-derived p-type GaN. The Mg-memory effect, and heterogeneous growth, substrate uniformity, and flux control are significant challenges for MOVPE and MBE, respectively. Photoluminescence (PL) of MOVPE-derived unintentionally doped (UID) heteroepitaxial GaN films show sharp lines near 3.478 eV due to recombination processes associated with the annihilation of free-excitons (FEs) and excitons bound to a neutral shallow donor (D/spl deg/X).