The kesterite thin film solar cells based on the quateary Cu2ZnSnS4 and Cu2ZnSnSe4 and their alloys Cu2ZnSn(S,Se)4 have been considered as environment-friendly and non-toxic alteatives to the currently commercialized CdTe and Cu(In,Ga)Se2 thin film solar cells. From the theoretical point of view, we will review how the group I2–II–IV–VI4 quateary compound semiconductors are derived from the binary CdTe and the teary CuInSe2 or CuGaSe2 through the cation mutation, and how the crystal structure and electronic band structure evolve as the component elements change. The increased structural and chemical freedom in these quateary semiconductors opens up new possibility for the tailoring of material properties and design of new light-absorber semiconductors. However, the increased freedom also makes the development of high-efficiency solar cells more challenging because much more intrinsic point defects, secondary phases, surfaces, and grain-boundaries can exist in the thin films and influence the photovoltaic performance in a way different from that in the conventional CdTe and Cu(In,Ga)Se2 solar cells. The experimental characterization of the properties of defects, secondary phase, and grain-boundaries is currently not very efficient and direct, especially for these quateary compounds. First-principles calculations have been successfully used in the past decade for studying these properties. Here we will review the theoretical progress in the study of the mixed-cation and mixed-anion alloys of the group I2–II–IV–VI4 semiconductors, defects, alkaline dopants, and grain boundaries, which provided very important information for the optimization of the kesterite solar cell performance.