We report on detailed calculations of quantum-size effects on the electronic structure of the valence-band regime and their manifestation in photoemission. Model calculations reveal the basic features of photoemission from quantum-well states (QWS). First, emission from QWS shows intensity variations with photon energy which is similar to that of semi-infinite systems, despite the discrete binding energies of the QWS. Second, conservation of the wave-vector component normal to the surface is directly related to the film thickness. Numerical calculations within the relativistic one-step model of photoemission show that these effects should be observable in 'real' systems. This is demonstrated to be the case for Cu films on fcc-Co(001). (C) 1999 Elsevier Science B.V. All rights reserved.