In the exploration of the nano-world of semiconductors there is a strong focus on low-dimensional structures and ultra-small devices. Two fundamental problems, which challenge progress in this field are: (i) large ensembles of nano-objects, like Quantum Dots (QDs), do not have identical geometrical shapes and electronic properties, and, (ii) the properties of a low-dimensional structure can be dominated by a few impurity atoms, whereas the properties of a macroscopic structure is determined by the quasi-continuous background of dopant impurities. To allow QDs and discrete impurities to be studied, novel experimental techniques are required. In this paper we describe how local luminescence has been excited from single QDs using electrons injected from a Scanning Electron Microscope (SEM), from the tip of a Scanning Tunneling Microscope (STM) or using highly focused photons for excitation. We present images of QDs as well as characteristic spectra of individual QDs. We finally show how the local character of the excitation enables us to excite and image individual impurities in low-dimensional structures, including the measurement of characteristic emission spectra from a single impurity atom in GaAs.