We have investigated intrinsic point defects in ZnO and extended this study to Li, Cu and Al impurity centres. Atomic and electronic structures as well as defect energies have been obtained for the main oxidation states of all defects using our embedded cluster hybrid quantum mechanical/molecular mechanical approach to the treatment of localised states in ionic solids. With these calculations we were able to explain the nature of a number of experimentally observed phenomena. We show that in zinc excess materials the energetics of zinc interstitial are very similar to those for oxygen vacancy formation. Our results also suggest assignments for a number of bands observed in photoluminescence and other spectroscopic studies of the material.