Prior to the advent of single-molecule fluorescence spectroscopy, many of the fundamental optical properties of colloidal semiconductor nanocrystal quantum dots were obscured by ensemble averaging over their inherent inhomogeneities. Single quantum dot spectroscopy has become a leading technique for the unambiguous determination of the governing excitonic physics of these quantum-confined systems. The analysis and interpretation of the timing and energies of photons emitted from individual nanocrystals have uncovered unexpected and fundamental electronic processes at the nanoscale. We review several different paradigms for deconstructing the photon stream from single nanocrystals, ranging from intensity "binning" techniques to more sophisticated methods based on single-photon counting. In particular, we highlight photon correlation - a powerful developing paradigm in single-nanocrystal studies. The application of photon-correlation techniques to single nanocrystals is changing the study of multiexcitonic recombination dynamics, uncovering the basic processes governing spectral linewidths and spectral diffusion, and enabling the extraction of single-nanocrystal properties directly from an ensemble with high statistical significance. These single-molecule techniques have proven invaluable for understanding the physics of nanocrystals and can provide unique insight into other heterogeneous and dynamical systems.