Organic–inorganic methylammonium lead halide perovskites have recently emerged as promising solar photovoltaic absorbers. In this Feature Article, we review our theoretical understanding of the superior photovoltaic properties, such as the extremely high optical absorption coefficient and very long carrier diffusion length of CH3NH3PbI3 perovskites through first-principles theory. We elucidate that the superior photovoltaic properties are attributed to the combination of direct band gap p–p transitions enabled by the Pb lone-pair s orbitals and perovskite symmetry, high iconicity, large lattice constant, and strong antibonding coupling between Pb lone-pair s and I p orbitals. We show that CH3NH3PbI3 exhibits intrinsic ambipolar self-doping behavior with conductivities tunable from p-type to n-type via controlling the growth conditions. We show that the p-type conductivity can be further improved by incorporating some group IA, IB, or VIA elements at I-rich/Pb-poor growth conditions. However, the n-type co...