Here we present the first comprehensive report on CdSe/CdS heterostructure nanocrystals. The effects of core size and shell thickness on the optical properties of CdSe/CdS heterostructure nanocrystals are investigated. We report a reliable synthetic method to grow thick CdS shells on CdSe cores with sizes ranging from 2.5-4.7 nm. We provide a calibration curve, which enables determination of CdS shell thickness (+/- 0.1 nm) over a wide range of core sizes, circumventing the need for time-consuming HRTEM analyses. Epitaxial growth of the shells was verified by HRTEM, XRD, and SAIED. In-situ reaction measurements revealed the average per particle (p) deposition rates for cadmium and sulfur to be k(Cd) = 5.38 x 10(-25) mol s(-1) p(-1) and k(s) = 4.83 x 10(-24) mol s(-1) p(-1). Faster sulfur deposition rates are attributed to the absence of strong sulfur binding ligands in the growth medium. Through the rigorous use of high resolution transmission electron microscopy, a direct link between the dimensions of the heterostructures and their band-edge transition energies, quantum yields, and excited state lifetimes is established. The experiments show that the band-edge transition energies of the core samples, which initially span approximately 431 meV, condense to span only 163 meV after the growth of a 6 monolayer-thick CdS shell. Furthermore, shifts in the band-edge transition energies were found to be extremely sensitive to core size. The QY of the as-prepared core/shells ranged from 25 to 60%. The QYs and band-edge lifetimes of the core/shells were found to depend upon the ligands adsorbed to the particle surface. These data prove that one or both of the charge carriers still has access to the particle surface despite the presence of a 2.2 nm thick CdS shell.