The surfaces of colloidal nanocrystals are complex interfaces between solid crystals, coordinating ligands, and liquid solutions. For fluorescent quantum dots, the properties of the surface vastly influence the efficiency of light emission, stability, and physical interactions, and thus determine their sensitivity and specificity when they are used to detect and image biological molecules. But after more than 30 years of study, the surfaces of quantum dots remain poorly understood and continue to be an important subject of both experimental and theoretical research. In this article, we review the physics and chemistry of quantum dot surfaces and describe approaches to engineer optimal fluorescent probes for applications in biomolecular imaging and sensing. We describe the structure and electronic properties of crystalline facets, the chemistry of ligand coordination, and the impact of ligands on optical properties. We further describe recent advances in compact coatings that have significantly improved their properties by providing small hydrodynamic size, high stability and fluorescence efficiency, and minimal nonspecific interactions with cells and biological molecules. While major progress has been made in both basic and applied research, many questions remain in the chemistry and physics of quantum dot surfaces that have hindered key breakthroughs to fully optimize their properties.