Low dimensional systems, such as nanodots, nanotubes, nanowires, have attracted great interest in the last years, due to their possible application in nanodevices. It is hence very important to describe accurately their electronic and optical properties within highly reliable and efficient ab-initio approaches. Density functional theory (DFT) has become in the last 20 years the standard technique for studying the ground-state properties, but this method often shows significant deviations from the experiment when electronic excited states are involved. The use of many-body Green's functions theory, with DFT calculations taken as the zero order approximation, is today the state-of-the-art technique for obtaining quasi-particle excitation energies and optical spectra. In this paper we will present the current status of this theoretical and computational approach, showing results for different kinds of low dimensional systems. (C) 2007 Elsevier B.V. All rights reserved.