Exciton transfer between two parallel GaAs V-groove quantum wires (QWRs) or two planar quantum wells (QWs) separated by AlGaAs barriers ranging from 5.5 nm to 20 nm thickness is studied by photoluminescence (PL) and PL excitation (PLE) spectroscopy. It is found that the transfer is strongly reduced between the widely spaced QWRs as compared with QWs. We have also investigated the optical absorption in single QWRs embedded in an AlGaAs V-shaped channel waveguide. Using a combination of PLE and absorption measurements we construct the full dependence of absorption spectra on the linear polarization. Our studies reveal the importance of inter-subband mixing in determining the energies of the light-hole-like transitions and thus the QWR absorption. Finally we present recent results on the fabrication and structural characterization of GaAs and GaP nanowires (NWs) grown by molecular beam epitaxy (MBE) on GaAs(111)B and Si(111) substrates, using Au-catalyzed vapor-liquid-solid growth technique. It is shown that, apart from optimizing the NW growth parameters, substrate material and the procedure for preparing the substrate before the MBE growth play an important role in controlling the NWs.