Since the seminal work by Kojima et al.in 2009,solar cells based on hybrid organic-inorganic perovskites have attracted considerable attention and experienced an exponential growth,with photovoltaic efficiencies as of today reaching above 22％.Despite such an impressive development,some key scientific issues of these materials,including the presence of toxic lead,the poor long-term device stability under heat and humidity conditions,and the anomalous hysteresis of the current-voltage curves shown by various solar cell devices,still remain unsolved and constitute an important focus of experimental and theoretical researchers throughout the world.Density functional theory calculations have been successfully applied to exploring structural and electronic properties of semiconductors,complementing the experimental results in search and discovery of novel functional materials.In this review,we summarize the current progress in perovskite photovoltaic materials from a theoretical perspective.We discuss design of lead-free perovskite materials,humidity-induced degradation mechanisms and possible origins for the observed solar cell hysteresis,and assess future research directions for advanced perovskite solar cells based on computational materials design and theoretical understanding of intrinsic properties.