Surface effects significantly influence the functionality of semiconductor nanocrystals. A theoretical understanding of these effects requires an atomic-scale description of the surface. We present an atomistic tight-binding theory of the electronic and optical properties of passivated and unpassivated CdS nanocrystals and CdS/ZnS core/shell nanocrystals. Fully passivated dots, with all dangling bonds saturated, have no surface states in the fundamental band gap, and all near-band-edge states are quantum-confined internal states. When surface anion dangling bonds are unpassivated, an anion-derived, narrow (bandwidth 0.05 eV), surface-state band lies 0.5 eV above the valence band edge, and a broader (0.2 eV) band of back-bonded surface states exists in the gap just above the valence band edge. When surface cation dangling bonds are unpassivated, a broad band of mixed surface/internal states exists above the conduction band edge. Partial passivation can push internal levels above the internal levels of a fully passivated dot or into the band gap. Because of this sensitivity to passivation, explicit models for surface effects are needed to describe accurately internal states. Capping the CdS dot with ZnS reduces the effect of the surface on the internal electronic states and optical properties. Six monolayers of ZnS are needed to eliminate the influence of any surface states on the internal states.