We present an overview of self-organised formation of lines of (semi)metal elements on semiconductor surfaces, together with an ab initio theoretical modelling of such quasi-one-dimensional systems. Results of calculations are presented for the atomic geometry, electronic states, and dispersion of the most tightly bound image state (IS) for a self-organised thin indium chain on the silicon surface forming the Si(1 1 1)-In(4 x 1) nanowire system. It is pointed out that strong anisotropic behaviour of the image state observed in inverse photoemission measurements originates from the anisotropy in the surface corrugation potential. Results are also presented for theoretically simulated STM images of self-organised Bi-lines on the Si(0 0 1) surface, which suggest a low density of states close to the valence band maximum localized on the Bi-lines, supporting a proposed model of a quantum antiwire system. (C) 2004 Elsevier B.V. All rights reserved.