We report on the density functional theory (DFT) modeling of core/shell quantum dot (QD) sensitized solar cells (QDSSCs), a device architecture that holds great potential in photovoltaics but has not been fully exploited so far. To understand the working mechanisms of this kind of solar cells, we have investigated ZnSe- and ZnSe/CdS-sensitized TiO2 models. Both the core-only and the core/shell QDs are predicted to strongly adsorb on the oxide surface, driven by the electrostatic interaction between the metal atoms on the QD surface and the O atoms exposed by the oxide substrate. Accordingly, the QD conduction states are strongly mixed with the TiO2 acceptor states, giving rise to bridge states that should funnel the interfacial electron transfer. Accordingly, quite fast electron injection processes are predicted, with computed rates of 135 and 163 fs. The back-electron transfer is much slower for ZnSe/CdS, due to the weak coupling between the newly injected charge and the holes trapped in the sensitizer core. Therefore, the core/shell QDs deliver much better efficiencies. Moreover, the interfacial dipole established between the TiO2-injected electrons and the holes confined in the QD are found to shift the conduction band edge of the oxide, which further improves the performance of the device in terms of the open circuit voltage (VOC). We believe that this work sets the ground for future computational works in the field, which could in turn guide the fabrication of new device architectures with improved efficiencies.