Self-ordering on crystal surfaces has been the subject of intense efforts during the last ten years. It has been recognized as a promising way for growing uniform nanostructures with regular sizes and spacings. Continuum models have been proposed where long-range elastic repulsive interactions are responsible for the periodic domain spontaneous formation. Vicinal surfaces unstable towards faceting lead to a one dimensional (1D) periodic morphology. Au(111) vicinals self-ordering provides a unique opportunity to point out the interplay between atomic and mesoscopic order. 2D ordering has been investigated in the complex case of atomic nitrogen adsorbed on Cu(100). Using scanning tunneling microscopy (STM) at elevated temperature, we have followed the ordered arrays of N square-shaped domains spontaneous formation. Observations are discussed in the light of previous continuum models for self-ordering. The question of understanding self-ordering is not only of fundamental but also of technological interest since it is a fruitful way of growing regularly spaced nanostructures in the 1-100 nm range. This will be illustrated by two examples: (i) self-ordered substrates can serve as templates for growing 2D square lattice of regular nanostructures; (ii) magnetic domains of an ultrathin film can be tailored by using self-ordered substrates. (C) 2002 Elsevier Science B.V. All rights reserved.