This paper deals first with recent experimental data on equilibrium step fluctuations on metal electrodes in contact with an electrolyte. The dynamics of steps on Cu(1 1 1) and Ag(1 1 1) electrodes is studied as a function of the electrode potential and temperature. From the Arrhenius-like temperature dependence of the fluctuations we deduce pre-exponential factors and activation energies for surface diffusion and dissolution processes. In the second part of the paper we discuss new results on island dynamics on Au(1 0 0) electrodes. From the time dependence of the island edge fluctuations and from the islands equilibrium shape we determine kink and step energies.