We review some recent results in the spectroscopy of single CdSe nanocrystal quantum dots. By eliminating the effects of inhomogeneous broadening and ensemble averaging, single nanocrystal spectroscopy has revealed many new and previously unexpected physical phenomena. Among those discussed in this review are ultra-narrow emission lineshapes (similar to 600x narrower than ensemble spectra), a highly polarizable emitting state in the presence of strong local electric fields, line broadening as a result of environmental fluctuations, and shifting of the emission spectra over a wide range of energies (from less than 300 mu eV to 80 meV). In addition, polarization spectroscopy of single nanocrystals has revealed the presence of a theoretically predicted two-dimensional transition dipole moment oriented in the xy plane of the nanocrystals. As a result, it is, in principle, possible to use polarization spectroscopy to determine the three-dimensional orientation of individual nanocrystals. These and other studies of single quantum dots have provided us with significant insight into the detailed physics and dynamics of this unique and fascinating physical system.