In the past 60 years development of photovoltaic semiconductors, the number of component elements has increased steadily, i.e., from silicon in the 1950s, to GaAs and CdTe in the 1960s, to CuInSe2 in the 1970s, to Cu(In, Ga) Se2 in the 1980s, to Cu2ZnSnS4 in the 1990s, and to recent Cu2ZnSn(S, Se)4 and CH3NH3PbI3. Whereas the material properties become more flexible as a result of the increased number of elements, and multinary compound semiconductors feature a dramatic increase of possible point defects in the lattice, which can significantly influence the optical and electrical properties and ultimately the photovoltaic performance. It is challenging to characterize the various point defects and defect pairs experimentally. During the last 20 years, first-principles calculations based on density functional theory (DFT) have offered an alternative method of overcoming the difficulties in experimental study, and widely used in predicting the defect properties of semiconductors. Compared with the available experimental methods, the first-principles calculations are fast, direct and exact since all possible defects can be investigated one by one. This advantage is especially crucial in the study of multinary compound semiconductors which have a large number of possible defects. Through calculating the formation energies, concentration and transition (ionization) energy levels of various possible defects, we can study their influences on the device performance and then identify the dominant defects that are critical for the further optimization of the performance. In this paper, we introduce the first-principles calculation model and procedure for studying the point defects in materials. We focus on the hybrid scheme which combines the advantages of both special k-points and -point-only approaches. The shortcomings of the presentcalculation model are discussed, with the possible solutions proposed. And then, we review the recent progress in the study of the point defects in two types of multinary photovoltaic semiconductors, Cu2ZnSn(S,Se)4 and H3NH3PbI3. The result of the increased number of component elements involves various competing secondary phases, limiting the formation of single-phase multinary compound semiconductors. Unlike ternary CuInSe2, the dominant defect that determines the p-type conductivity in Cu2ZnSnS4 is Cu-on-Zn antisite (CuZn) defect rather than the copper vacancy (VCu). However, the ionization level of CuZn is deeper than that of VCu. The self-compensated defect pairs such as [2CuZn+SnZn] are easy to form in Cu2ZnSnS4, which causes band gap fluctuations and limits the Voc of Cu2ZnSnS4 cells. Additionally the formation energies of deep level defects, SnZn and VS, are not sufficiently high in Cu2ZnSnS4, leading to poor lifetime of minority carriers and hence low Voc. In order to enhance the formation of VCu and suppress the formation of CuZn as well as deep level defects, a Cu-poor/Zn-rich growth condition is required. Compared with Cu2ZnSnS4, the concentration of deep level defects is predicted to be low in Cu2ZnSnSe4, therefore, the devices fabricated based on the Se-rich Cu2ZnSn(S,Se)4 alloys exhibit better performances. Unlike Cu2ZnSnS4 cells, the CH3NH3PbI3 cells exhibit rather high Voc and long minority-carrier life time. The unusually benign defect physics of CH3NH3PbI3 is responsible for the remarkable performance of CH3NH3PbI3 cells. First, CH3NH3PbI3 shows that flexible conductivity is dependent on growth condition. This behavior is distinguished from common p-type photovoltaic semiconductor, in which the n-type doping is generally difficult. Second, in CH3NH3PbI3, defects with low formation energies create only shallow levels. Through controlling the carrier concentration (Fermi level) and growth condition, the formation of deep-level defect can be suppressed in CH3NH3PbI3. We conclude that the predicted results from the first-principles calculations are very useful for guiding the experimental study.