We address the problem of the departure of a crystal surface from a pe
rfectly ordered crystal plane. We discuss the energetics of the surfac
e defects and their statistical mechanics which lead to the so-called
''roughening transition''. The theory of this transition is outlined a
nd a special emphasis is put on the experimental aspects: roughening m
easurement techniques and critical review of the available data. We pa
y special attention to the case of vicinal surfaces. Apart from the eq
uilibrium situation there is an increasing interest in the dynamical r
oughening of crystal surfaces during MBE growth or ion-bombardment etc
hing, or in the reverse problem: the annealing of a non-equilibrium ro
ughness. We review the present state of this field by recalling releva
nt models which lead to the concept of dynamical scaling and we discus
s some recent data. The present review is restricted to the case of me
tal surfaces; however, most of the concepts which are presented have a
much larger generality.