ZnO single crystal thin films were grown on c-plane sapphire using oxygen microwave plasma assisted molecular beam epitaxy. Atomically flat oxygen-terminated substrate surfaces were obtained by pre-growth cleaning procedures involving an oxygen plasma treatment. A two dimensional nucleation during the initial growth which is followed by a morphology transition to three dimensional nucleation was observed by in situ reflection high energy electron diffraction. X-ray diffraction (XRD) and photoluminescence investigations suggest that the ZnO epilayer consists of a high quality layer on top of a transition layer containing a high density of defects in the interfacial region. A full width at half maximum (FWHM) of 0.005° is obtained for the ZnO(0002) diffraction peak in an XRD rocking curve, while a broad tail extending from the peak can also be observed. The photoluminescence spectra exhibit dominant bound exciton emission with a FWHM of 3 meV at low temperatures and free exciton emission combined with a very weak deep level emission at room temperature. Recently, these high quality ZnO epilayers have allowed the observation of optically pumped lasing at room temperatures as well as stimulated emission up to 550 K, both of which are due to an exciton related mechanism.