  In the past perfect surfaces have been shown to yield a local critical
behaviour that differs from the bulk critical behaviour. On the other hand
surface defects, whether they are of natural origin or created artificially,
are known to modify local quantities. It is therefore important to clarify
whether these defects are relevant or irrelevant for the surface critical
behaviour.
  The purpose of this review is two-fold. In the first part we summarise some
of the important results on surface criticality at perfect surfaces. Special
attention is thereby paid to new developments as for example the study of
surface critical behaviour in systems with competing interactions or of surface
critical dynamics. In the second part the effect of surface defects (presence
of edges, steps, quenched randomness, lines of adatoms, regular geometric
patterns) on local critical behaviour in semi-infinite systems and in thin
films is discussed in detail. Whereas most of the defects commonly encountered
are shown to be irrelevant, some notable exceptions are highlighted. It is
shown furthermore that under certain circumstances non-universal local critical
behaviour may be observed at surfaces.
