Photoluminescence (PL) spectroscopy and associated techniques are used to investigate the optical properties of zinc oxide (ZnO) samples. For samples grown by the pulsed laser deposition (PLD) technique we see evidence from PL measurements that they are of reasonably good quality, showing strong band-edge emission at both room and low temperatures. The low temperature PL is mainly due to near bandedge emission which increases in intensity with the annealing temperature of the PLD samples, which is interpreted as due to the increase in crystallite size and quality with annealing. We comment on the effects of strain and electric fields on the PL spectra as a function of annealing. Some evidence is also seen to favour the oxygen vacancy model of the green band. The PLD-grown material was referenced against a commercially grown bulk ZnO material of high quality. An investigation into the processes involved in ZnO when it is optically pumped with high excitation values is undertaken. Identifications of the various non-linear features seen are presented. Measurements of optically pumped stimulated emission from the bulk material and PLD-grown samples have been made using an Nd: YAG laser. We discuss the results of high intensity optical excitation of both the bulk crystal and nanocrystalline samples. The effect of the various grain sizes in the PLD material on the emission processes is discussed. Lasing effects in these samples are identified and the nature of the processes examined, the origin of the laser cavity in the ZnO samples is discussed in relation to models of random lasing from the literature. We also comment in particular on the possible reasons why we fail to see any lasing effects in the bulk sample and present a simple model, which may partly answer this question.