We review our current understanding of the reversible phase transitions found in
clean semiconductor and metal/semiconductor surfaces. The most important
phase transitions are considered in detail, in particular those appearing in Si(001),
Ge(001), Si(111), Ge(111), 3C-SiC(001), Pb and Sn on Si(111) and Ge(111),
Au/Si(111) and Ag/Si(111). Special emphasis is placed on recent experiments and
theoretical models, as well as on open or controversial aspects of these interesting
surface systems.