The spectroscopic properties of core/shell structured ZnTe/CdSe nanocrystals (NCs) have been systematically studied. By varying the ZnTe core diameter and the CdSe shell thickness, the absorption onset and the photoluminescence peak position of the ZnTe/CdSe NCs can be readily tuned over a wide range. The theoretical model based on an effective mass approximation demonstrates that the ZnTe/CdSe NCs have type II carrier localization in which the photoexcited electrons and holes are spatially separated and confined in the shell and core, respectively. The energetics of the conduction and valence bands and the bandgaps of the ZnTe/CdSe NCs are accurately predicted. The photoluminescent experiments show that electron quenchers having a large energy difference between their reduction potential and the lowest conduction band edge of the ZnTe/CdSe nanocrystals can completely quench the luminescence. Electron acceptors having a reduction potential only slightly below the conduction band edge partially quench the photoluminescence of the nanocrystals. In this case, the extent of quenching depends upon the thickness of the shell and the energy difference. Despite the confinement of photoexcited holes in the core, the photoluminescence could be still quenched by adsorbed hole quenchers. The extent of hole quenching depends upon the core size, the shell thickness and the oxidation potential of the quenchers. Basically, an increase in the core size and the shell thickness may lead to a decrease in the extent of hole quenching. The work presented here is of great interest since it can be extended to understand the spectroscopic properties and photoluminescence quenching behaviors of other core/shell semiconductor NCs.