Carbonates have been known to act as hydrocarbon source rocks, but their basic geochemical and associated hydrocarbon generation characteristics remain not well understood as they occur with argillaceous source rocks in most cases, and the hydrocarbon generation from each rock type is difficult to distinguish, forming one of puzzling issues within the field of petroleum geology and geochemistry. To improve the understanding of this critical issue, this paper reviews recent advances in this field and provides a summary of key areas that can be studied in future. Results show that carbonate source rocks are generally associated with high-salinity environments with low amounts of terrestrial inputs and low dissolved oxygen contents. Petrographically, these source rocks are dark gray or black, fine-grained, stratified, and contain bacterial and algal bioprecursors along with some other impurities. They generally have low organic matter contents, although these can vary significantly in different cases (e.g., the total organic carbon contents of marine and lacustrine carbonate source rocks in China are generally 0.1%–1.0% and 0.4%–4.0%, respectively). These rocks contain type I and type II kerogen, meaning there is a lack of vitrinites. This means that assessment of the maturity of the organic matter in these sediments needs to use non-traditional techniques rather than vitrinite reflectance. In terms of molecular geochemistry, carbonate source rocks have typical characteristics indicative of generally reducing and saline environments and lower organism-dominated bioprecursors of organic matter, e.g., high contents of sulfur compounds, low Pr/Ph ratios, and dominance of n-alkanes. Most of the carbonate source rocks are typically dominated by D-type organic facies in an oxidized shallow water mass, although high-quality source rocks generally contain A- and B-type organic facies in saline lacustrine and marine-reducing environments, respectively. The hydrocarbon generation model for the carbonate source rocks can involve early, middle, and late stages, with a diversity of hydrocarbons within these rocks, which can be aggregated, adsorbed, enclosed within minerals, or present as inclusions. This in turn implies that the large-scale hydrocarbon expulsion from these rocks is reliant on brittle deformation caused by external forces. Finally, a number of aspects of these source rocks remain unclear and need further study, including the effectiveness of carbonates as hydrocarbon source rocks, bioprecursors, and hydrocarbon generation models of carbonate source rock, and the differences between marine and lacustrine carbonate source rocks.