The history of tight-binding theory is traced, from the corresponding
band models of Bloch, to the development of universal parameters, deri
vable from a combination of tight-binding theory and free-electron the
ory. In the end, tight-binding theory becomes an independent, and in t
hat sense ab initio, method for studying virtually all of the properti
es of surfaces. It is this conceptual aspect, rather than semiempirica
l tight-binding theory as an approximate computational method, which i
s emphasized here. We outline the application first to surface energy,
and its dependence upon structure, for semiconductors, ionic insulato
rs, and simple metals, finding wide differences from the rudimentary v
iew of one bond energy per broken bond. We turn to photothresholds, wo
rk functions and electron affinities, finding direct tight-binding pre
dictions but necessary corrections for image potentials, which also ar
e derivable in terms of tight-binding theory. For the particular case
of electron affinities there are additional corrections to the band ga
p, usually associated with correlation energy, but readily and general
ly estimated as the intra-atomic Coulomb U divided by the dielectric c
onstant. We turn to history of the understanding of heterojunction ban
d line-ups, which in the end can be obtained by matching ''neutrality
levels'' in each band structure, those levels being the average sp(3)-
hybrid energy in tight-binding theory and in the case of metals, the F
ermi energy. Alternate views are also discussed as is the bonding of i
ndividual atoms to the surface. Finally, the successes and failures of
tight-binding theory in understanding semiconductor surface reconstru
ctions are reviewed.