Nanostructured surfaces are of fundamental importance in an ever-increasing number of applications. Strategies based on self-organization are a promising route for the controlled fabrication of nanostructured objects. Indeed, self-organization appears to be a much more frequent behavior than presumed and could be seen as a rule more than an exception. Nevertheless, in order to be practical and usable, the ability to tailor the size and dimensionality of the grown nanostructures is a prerequisite. This involves a full understanding of the fundamental aspects controlling self-organization mechanism. The parameters governing the growth of self-organized surfaces are not yet fully understood. This may explain why their use is still limited. This review discusses a prototypical self-organized surface, namely, the O/Cu (110)-( 2 x 1) surface and identifies the parameters which control the self-organization process and how they can be tuned. It is shown how these parameters can be varied by controlled co-adsorption of species at the surface in order to tailor the self-organization process and extend the range of achievable nanostructures.