||In this thesis, the growth of patterned ZnSe nanowire arrays on the GaAs (111) substrate is studied. Arrays of catalyzing gold particles are first patterned on the GaAs (111) substrate and the growth of ZnSe nanowires is then carried out using the Molecular Beam Epitaxy (MBE) technique. It is found that the size of the ZnSe nanowires could be controlled by the size of the catalyzing gold particles, but control on the nanowire orientations can only be achieved with gold particles that are patterned on carefully deoxidized GaAs (111) substrate. Under appropriate conditions, ZnSe nanowires grew predominantly vertical to the substrate surface. However, a small fraction of the nanowires was found with their directions inclined to the substrate surface. The presence of these inclined nanowires is attributed to the nanowires grown along other members of <111> family and the formation of twin defects in the initial stage of nanowire growth. The growth rates of nanowires have been measured for nanowires with several different diameters. The results are compared to the predictions of existing models for the Vapor-Liquid-Solid (VLS) process involved in nanowire growth. The photoluminescence spectra obtained at 50K from the nanowire array containing 6 nm and 80 nm nanowires showed two band to band emission peaks at 410nm and 448nm and two defect related peaks at 546nm and 614nm. The blue-shift between the 410nm and 448 nm peaks is 250 mV, the same as the blue-shift between the 546 nm and 614 nm peaks. We ascribe the 410 nm and 546 nm peaks to the 6 nm nanowires and the 448 nm and 614 nm peaks to the 80 nm nanowires. The measured blue-shift agrees well with that expected from quantum size confinement effect.