Semiconductor nanocrystals, the so-called quantum dots (QDs), exhibit versatile optical and electrical properties. However, QDs possess high density of surface defects/traps due to the high surface-to-volume ratio, which act as nonradiative carrier recombination centers within the QDs, thereby deteriorating the overall solar cell performance. The surface passivation of QDs through the growth of an outer shell of different materials/compositions called "core/shell QDs" has proven to be an effective approach to reduce the surface defects and confinement potential, which can enable the broadening of the absorption spectrum, accelerate the carrier transfer, and reduce exciton recombination loss. Here, the recent research developments in the tailoring of the structure of core/shell QDs to tune exciton dynamics so as to improve solar cell performance are summarized. The role of band alignment of core and shell materials, core size, shell thickness/compositions, and interface engineering of core/thick shell called "giant" QDs on electron-hole spatial separation, carrier transport, and confinement potential, before and after grafting on the carrier scavengers (semiconductor/electrolyte), is described. Then, the solar cell performance based on core/shell QDs is introduced. Finally, an outlook for the rational design of core/shell QDs is provided, which can further promote the development of high-efficiency and stable QD sensitized solar cells.