Zinc oxide (ZnO) is a wide band gap semiconductor material with attractive features for light emitting devices, photovoltaics, chemical sensors and spintronics. In the past 10 yr ZnO has attracted tremendous interest from the materials science and semiconductor physics research communities, and in this review recent progress in (i) bulk growth, (ii) understanding of the role of hydrogen and (iii) formation of high-quality Schottky barrier (SB) diodes, are discussed for single crystalline ZnO. In (i), the emphasis is put on hydrothermally grown material and how the concentration of intentional and unintentional impurities, such as In and Li, can be controlled and modified by high temperature treatment and defect engineering involving vacancy clusters. In (ii), different possible configurations of hydrogen as a shallow donor are evaluated based on results from calculations employing the density-functional-theory as well as from experimental studies of local vibrational modes using Fourier transform infrared spectroscopy. Further, hydrogen is demonstrated to be very reactive and the interaction with zinc vacancies, group I and group V elements, and transition metals are elucidated. Moreover, the diffusion of hydrogen is found to be rapid and limited by the concentration of traps in hydrothermal samples, and it is argued that isolated (free) hydrogen is not very likely to exist in ZnO at room temperature. In (iii), a compilation of the literature data illustrates that the SB heights for metals deposited on n-type samples have no correlation with the metal work function, violating the fundamental Schottky–Mott model. The role of surface preparation cannot be overestimated and in several cases an oxidation of the surface prior to metal deposition is shown to be beneficial for the formation of high barrier SB diodes. The effects of near-surface defects, such as oxygen vacancies, and contact inhomogeneity are also addressed. However, in spite of the significant progress made in the past 5–7 years, a thorough understanding of the SB formation to ZnO is still lacking. Finally, results from characterization of electrically active point defects employing the SB contacts and junction spectroscopic techniques are reviewed and the identification of some prominent bandgap states is critically evaluated.