In the present work, we review some recent advances on computer simulation devoted to understand different aspects of electrochemical nanostructuring and surface phase formation. Top-down and bottom-up methods are discussed. Concerning the first approach, a short introduction presents the most common experimental techniques employed for electrochemical nanostructuring, discussing the status of theoretical modeling for them. Among these techniques, reference is made to tip-induced local metal deposition (TILMD), defect-induced local metal deposition (DILMD), tip-induced electrochemical nucleation (TIEN), tip-induced electronic contact dissolution (TIECD) and scanning electrochemical microscopy (SECM). Detailed discussion is provided on recent advances on the simulation of TILMD and DILMD by means of atom dynamics and off-lattice Grand Canonical Monte Carlo methods for a number of systems, drawing general trends. Concerning bottom-up approaches, the application of lattice Monte Carlo methods to this problem is addressed. Both thermodynamic and kinetic lattice Monte Carlo applications are discussed in relation to metal deposition on foreign substrates with and without surface defects. (c) 2005 Elsevier Ltd. All rights reserved.