We report a synthesis of highly luminescent (CdSe)ZnS composite quantum dots with CdSe cores ranging in diameter from 23 to 55 Angstrom. The narrow photoluminescence (fwhm less than or equal to 40 nm) from these composite dots spans most of the visible spectrum from blue through red with quantum yields of 30-50% at room temperature. We characterize these materials using a range of optical and structural techniques. Optical absorption and photoluminescence spectroscopies probe the effect of ZnS passivation on the electronic structure of the dots. We use a combination of wavelength dispersive X-ray spectroscopy, X-ray photoelectron spectroscopy, small and wide angle X-ray scattering, and transmission electron microscopy to analyze the composite dots and determine their chemical composition, average size, size distribution, shape, and internal structure. Using a simple effective mass theory, we model the energy shift for the first excited state for (CdSe)ZnS and (CdSe)CdS dots with varying shell thickness. Finally, we characterize the growth of ZnS on CdSe cores as locally epitaxial and determine how the structure of the ZnS shell influences the photoluminescence properties.