A series of our studies are reviewed on quantized electronic states confined in thin metal films on semiconductor surfaces, investigated by scanning tunneling microscopy and angle-resolved photoemission spectroscopy. Atomically flat and epitaxial Ag(111) films of 5 - 30 atomic layer thick grew on Si(001)2 × 1 and Si(111)7 × 7 clean substrates by depositing Ag at about 100 K and subsequent annealing up to 300 - 450 K. Discrete Ag 5s states were observed at binding energies of 0.3 - 3 eV below Fermi level, whose energy positions depended on the film thickness, together with the thickness-independent surface state of Ag(111). The discrete electronic states are interpreted in terms of the quantum-well states (QWS) based on the phase-shift quantization rule. The phase shift, energy dispersion, and energy-versus-thickness relation (Structure Plot) of the QWS's were consistently derived. On the other hand, for the in-plane dispersion, in contrast to the expected free-electron-like behavior, the QWS's showed (i) a significant enhancement of the in-plane effective mass with decreasing binding energy, and (ii) a splitting of a QWS into two electronic states having different dispersions at off-Γ points. Such unexpected properties of the QWS were found obviously related to an interaction with the Si substrate band structure. The QWS splitting is explained by the energy dependence in reflection phase shift at the film-substrate interface occurring at the substrate band edge. [DOI: 10.1380/ejssnt.2004.169]