We have investigated the structural, electronic and magnetic properties of some prototypical examples of GaAs-based nanostructures. We focus on two kashida; TEXT-ALIGN: justify; TEXT-KASHIDA: 0%; MARGIN: 0cm 0cm 0pt; unicode-bidi: embed; DIRECTION: ltr; mso-layout-grid-align: none" The motivation for the choice of GaAs originates from the fact that the GaAs-based technology is nowadays well established and large effort is devoted to the design of GaAs-based modern electronic devices. In this thesis we focus on the computational and theoretical modeling of GaAs-based nanostructures. Engineering complex materials and devices down to the nano-scale strongly requires an atomic-scale investigation of their properties. The contribution of computational/theoretical studies is nowadays essential to their understanding, thanks to predictive power of state-of-the-art modelling techniques. Ab initio electronic structure calculations are employed since the quantum mechanical behaviour of the electrons is explicitly relevant in these structures. The PWscf (Plane-Wave Self-Consistent Field) computer code for electronic-structure calculations within Density-Functional Theory, developed and maintained by a research team mainly from the Scuola Internazionale Superiore di Studi Avanzati and the DEMOCRITOS National Simulation Center in Trieste (Italy) has been used for the research presented here. Massively parallel super-computers have been used since the systems studied are computationally demanding in terms of CPU time and memory usage.