The polarity of heteroepitaxial ZnO films is controlled by interface engineering. The ZnO films are grown on Ga-polar GaN templates by plasma-assisted molecular beam epitaxy. By forming a ZnO/GaN heterointerface without any interfacial layer through Zn pre-exposure, Zn-polar ZnO films are grown. O-polar ZnO films are obtained by forming a Ga2O3 interfacial layer, with an inversion center, in between the ZnO and GaN through O-plasma pre-exposure. A polarity inverted ZnO heterostructure is fabricated, without the formation of inversion domain boundaries, by inserting a MgO layer with an inversion center between the lower and upper ZnO layers. Mosaic tilt and twist angles of Zn- and O-polar ZnO films are, respectively, 0.10degrees and 0.18degrees (tilt), and 0.25degrees and 0.32degrees (twist). Dislocation densities in Zn-polar ZnO films are lower than those in O-polar ZnO films from both high resolution x-ray diffraction,and transmission electron microscopic evaluation. A higher Ga-doping efficiency in the O-polar ZnO films than in the Zn-polar ZnO films was determined by two-layer Hall-effect analyses and photoluminescence intensities of Ga-related donor bound exciton emission. Free exciton emissions are observed from both undoped Zn-and O-polar ZnO films with narrower linewidths of bound exciton emissions from the Zn-polar ZnO films. Relative redshifts of bound exciton emissions from the O-polar ZnO films compared with those from the Zn-polar ZnO films are consistently observed for the undoped and Ga-doped ZnO films.