As colloidal semiconductor nanocrystals are developed for a wider range of diverse applications, it becomes more important to gain a deeper understanding of their properties in order to direct synthetic efforts. While most synthetic developments are guided by changes in ensemble properties, certain applications such as those in nano-electronics and nano-photonics rely on properties of nanocrystals at the individual level. For such applications and even for a more detailed understanding of the ensemble behavior, single nanocrystal spectroscopy becomes a vital tool. This review looks at how single nanocrystal spectroscopy has been applied to materials based on modern synthetic techniques and how these studies are elucidating properties that remain hidden at the ensemble level. First, recent theoretical models that are important for understanding many observed phenomena are explored. Then the review highlights new insights into many of the photophysical properties that are of interest in semiconductor nanocrystal materials, such as the ubiquitous spectral instability, magneto-optical identification of the band-edge exciton fine structure, emission from multi-excitons, and the spectroscopic properties of charged nanocrystals that challenge long standing theories on photoluminescence blinking behavior. To date most of the research has been conducted on materials based on cadmium selenide primarily due to its many years of development as a prototypical nanocrystal system. The review ends with a discussion of new materials that would also benefit from a detailed photophysical understanding afforded by single nanocrystal spectroscopy.