The investigation of step and island dynamics on surfaces has enormously co
ntributed to the microscopic understanding of mass transport processes in e
quilibrium, during growth and coarsening of surface structures. From the sc
aling behavior of step fluctuations as well as of the ripening of mono- and
multilayer islands, the atomic diffusion processes may be unambiguously de
termined even when single atom motion cannot be observed directly. This is
the case for metal surfaces at high temperatures and, in particular, for me
tal electrodes in electrochemical environment. In the case of the latter, t
he analysis of step and island dynamics is the only method available to dat
e to learn about the dynamics at the solid/liquid interface on the atomic s
cale. Here, we review the basic theoretical principles and the experimental
contributions on step and island dynamics performed in ultra-high vacuum a
s well as (more recently) in electrolyte. It focuses also on the comparison
between experimental results obtained at the solid/vacuum and at the solid
/liquid interface. (C) 2001 Elsevier Science Ltd. All rights reserved.