Phase pure and clean MgB2 films have been fabricated on different types of single-crystal substrate, including SiC, sapphire, MgO,LaAlO3,SrTiO3, andyttrium-stabilized ZrO2 (YSZ), via the hybrid physical–chemical vapor deposition (HPCVD) technique. PureMgB2 films with different structural textures are obtained by selectingthe substrate and its orientation, such as off-axis epitaxialMgB2 on MgO(211) ortextured MgB2 on YSZ(110)substrates. Films show Tc(0) in the range 37–41 K, and residual resistivityρ(42 K) between0.3 and 5 µΩ cm as the substrate and film thickness are varied. The crystal structures and filmmorphologies are presented and discussed. Further investigations are focused onc-axis epitaxialfilms. Epitaxial MgB2 films with thickness about 300 nm manifestTc(0) = 41.2 K and residualresistivity ρ(42 K) = 0.35 µΩ cm onSiC(0001) while Tc(0) = 39.5 K and ρ(42 K) = 0.27 µΩ cm on c-cut sapphire, reflecting that the films are of high quality and in the ‘clean limit’. Lowupper critical field and large anisotropy of the upper critical fieldγ comparable tothe results from MgB2 single crystals are also revealed. The smooth surface of the epitaxial films, withroot-mean-square (RMS) roughness less than 5 nm, makes them well qualifiedfor device applications. Microwave performance measurements are carried outusing a coplanar resonator on a 300 nm thick film on sapphire substrate and nopower dependence of unloaded quality factor in the output power range of−10–25 dB is found.