Recently, Fickenscher et al.  have shown that, in a core-multi-shell structure where a GaAs quantum well is embedded into an AlGaAs shell wrapped around a  oriented GaAs nanowire, the electron and hole ground states are strongly confined to the corners of the hexagonally symmetric quantum well. Thus this confinement defines quantum wires which run along the length of the nanowires along its corners. Here we review single nanowire photoluminescence measurements which show the significant confinement energy of the excitons. For well widths larger than 5 nm, optical transitions between electron and hole excited states can be seen in excitation spectra, while for widths less than 5 nm only the ground state optical transitions are observed. For well widths smaller than 5 nm, high resolution spatially resolved photoluminescence measurements show directly the appearance of localized states. Single nanowire spectra from the 4 nm QWT sample display ultranarrow emission lines on the high energy side of the luminescence band. Spatially-resolved PL images show that these quantum dots are localized randomly along the length of the wire.