The evolution of the surface Green function matching (SGFM) method is
reviewed in relation to the experimental and computational development
s which influenced its evolution or changed its scope. Starting with e
lectronic surface/interface states, the theory is extended to arbitrar
y elementary excitations. The other extension of the formalism is from
continuous to discrete media. Finally, the extension from single to m
ultiple interfaces provides a way of dealing with the new layered syst
ems, e.g., quantum wells and superlattices.