The electronic structure of the thiolate-protected gold clusters is characterized by strongly pronounced quantum effects. These result in discrete electronic states, and a nonzero HOMO/LUMO gap. This existence of discrete electronic states was first indicated by the discrepancy between their optical absorption and the predictions of classical Mie scattering. The discrete optical transitions and occurrence of photoluminescence in these species are areas where they behave like molecular, rather than metallic, substances. This molecular optical behavior sharply distinguishes thiolate-protected clusters from gold nanoparticles, whose optical characteristics are driven by Plasmon resonance. Some of thiolate-protected clusters properties can be described using a model in which the clusters are treated like "superatoms". According to this model they exhibit atomic-like electronic states, that are labeled S,P,D,F according to their respective angular momentum on the atomic level. Those clusters that have a "closed superatomic shell'" configuration have indeed been identified as the most stable ones. This electronic shell closure and the resulting gain in stability is responsible for the discrete distribution of a few stable cluster sizes (magic numbers) observed in their synthesis, rather than a quasi-continuous distribution of sizes.