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 AlZn, 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 NO 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 (NO), and more complicated acceptor structures, such as AsZn-2VZn, 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.