Despite the exciting progress on power conversion efficiencies, the commercialization of the emerging lead (Pb) halide perovskite solar cell technology still faces significant challenges, one of which is the inclusion of toxic Pb. Searching for Pb-free perovskite solar cell absorbers is currently an attractive research direction. The approaches used for and the consequences of Pb replacement are reviewed herein. Reviews on the theoretical understanding of the electronic, optical, and defect properties of Pb and Pb-free halide perovskites and perovskite derivatives are provided, as well as the experimental results available in the literature. The theoretical understanding explains well why Pb halide perovskites exhibit superior photovoltaic properties, but Pb-free perovskites and perovskite derivatives do not.