The intricate chemistry occurring at the surface of semiconductor nanocrystals is crucial to tailoring their optical properties to a myriad of applications. This perspective aims to re-evaluate long held ideas in semiconductor nanocrystal surface science in the light of a body of new and rich research. We start by reviewing recent developments in ligand chemistry, followed by a discussion of spectroscopic and computational approaches used for advancing the poorly-understood electronic structure of the surface. With the insights gained, we show how the surface impacts emissive behaviour and we summarize strategies to increase fluorescent quantum yield. This discussion is followed by a review of experimental approaches for quantitative analysis of the surface chemistry at concentrations relevant to spectroscopic measurements. We end by highlighting some new directions in ligand chemistry, namely all-inorganically passivated semiconductor nanocrystals and new applications of surface emission.