After decades of work, the growth of continuous thin films, i.e., two-dimensional structures, is progressively becoming a technological issue more than a field of fundamental research. Incidentally self-organization of nanostructures on surfaces is now an important field of research, i.e., structures of dimensionality one or zero, with a steep rise of attention in the past five years. Whereas self-organization was initially motivated by potential applications, it has up to now essentially contributed to the advancement of fundamental science in low dimensions, as model systems could be produced that could not have been fabricated by lithography. This Special Issue aims at giving a cross-community timely overview of the field. The Issue gathers a broad panel of articles covering various self-organization mechanisms, specific structural characterization, physical properties, and current trends in extending the versatility of growth. The materials mostly covered here are semiconductors and magnetic materials.