Colloidal semiconductor nanocrystals become increasingly important in materials science and technology, due to their optoelectronic properties that are tunable by size. The measurement and understanding of their energy levels is key to scientific and technological progress. Here we review how the confined electronic orbitals and related energy levels of individual semiconductor quantum dots have been measured by means of scanning tunneling microscopy and spectroscopy. These techniques were originally developed for flat conducting surfaces, but they have been adapted to investigate the atomic and electronic structure of semiconductor quantum dots. We compare the results obtained on colloidal quantum dots with those on comparable solid-state ones. We also compare the results obtained with scanning tunneling spectroscopy with those of optical spectroscopy. The first three sections provide an introduction to colloidal quantum dots, and a theoretical basis to be able to understand tunneling spectroscopy on dots attached to a conducting surface. In sections 4 and 5, we review the work performed on lead-chalcogenide nanocrystals and on colloidal quantum dots and rods of II-VI compounds, respectively. In section 6, we deal with colloidal III-V nanocrystals and compare the results with their self-assembled counter parts. In section 7, we review the work on other types of semiconductor quantum dots, especially on Si and Ge nanocrystals.