After summing up the main physical properties of ZnO and its subsequent applications the aim of this article is to review the growth of ZnO epitaxial films by PLD, MBE, MOCVD and sputtering under their various aspects, substrates, precursors, reaction chemistry, assessment of the layers etc...., keeping constantly in mind some key issues for the device applications of ZnO in optoelectronics, surface acoustic filters and spintronics, amongst which the growth of high quality epitaxial layers of both n- or p-type conductivity, the possibility of dissolving transition elements in the layers, the growth of ZnO related alloys and heterostructures are of major significance. (c) 2005 Elsevier Ltd. All rights reserved.