Lead halide perovskites have recently emerged as promising absorbers for fabricating low-cost and high-efficiency thin-film solar cells. The record power conversion efficiency of lead halide perovskite-based solar cells has rapidly increased from 3.8% in 2009 to 22.1% in early 2016. Such rapid improvement is attributed to the superior and unique photovoltaic properties of lead halide perovskites, such as the extremely high optical absorption coefficients and super-long photogenerated carrier lifetimes and diffusion lengths that are not seen in any other polycrystalline thin-film solar cell materials. In the past a few years, theoretical approaches have been extensively applied to understand the fundamental mechanisms responsible for the superior photovoltaic properties of lead halide perovskites and have gained significant insights. This review article highlights the important theoretical results reported in literature for the understanding of the unique structural, electronic, optical, and defect properties of lead halide perovskite materials. For comparison, we also review the theoretical results reported in literature for some lead-free perovskites, double perovskites, and nonperovskites.