In recent years, ZnO has been proposed for new electronic and optoelectronic devices, such as transparent transistors and UV light-emitting diodes (LEDs). The LED application will require both n-type and p-type ZnO, but the latter is difficult to produce, and progress in this area will require a detailed knowledge of the various impurities and defects that affect the electrical and optical properties. The dominant donors in as-grown ZnO are usually thought to be interstitial H and substitutional Al-Zn with activation energies of about 40 and 65 meV, respectively. However, interstitial Zn and its associated complexes may also contribute free electrons. The dominant acceptor, at least in vapor-phase-grown material, is the Zn vacancy; however, substitutional N-O is also present, although sometimes passivated by H. To produce p-type ZnO, it is necessary to dope with acceptor-type impurities, and some success has been achieved with N, P, As, and Sb. However, only N has been proven to have simple substitutional character (N-O), and more complicated acceptor structures, such as As-Zn-2V(Zn) have been proposed for some of the other group V elements. Both homostructural and heterostructural UV LEDs have been fabricated, although not of high luminescent power so far. The main objective of this paper is to review the Hall-effect and photoluminescence results on n-type and p-type ZnO.