For the past several decades, a relative potency approach has been used to estimate the human health risks from exposure to polycyclic aromatic hydrocarbon (PAH) mixtures. Risk estimates are derived using potency equivalence factors (PEFs; also called relative potency factors [RPFs]), based on the ratio of selected PAHs to benzo[a]pyrene (BaP), expressed qualitatively by orders of magnitude. To quantify PEFs for 18 selected carcinogenic PAHs, a systematic approach with a priori and dose response criteria was developed, building on draft work by the US EPA in 2010 and its review by US EPA Science Advisory Board (SAB) in 2011. An exhaustive search for carcinogenicity studies that included both target PAHs and BaP with environmentally relevant exposure routes found only 48 animal bioassay datasets (mostly pre-1992 based on skin painting). Only eight datasets provided adequate low-response data, and of these only four datasets were appropriate for modeling to estimate PEFs; only benzo[b]fluoranthene and cyclopenta[c,d]pyrene had a PEF that could be quantified. Thus, current knowledge of PAH carcinogenicity is insufficient to support quantitative PEFs for PAH mixtures. This highlights the long-acknowledged need for an interdisciplinary approach to estimate risks from PAH mixtures. Use of alternative and short-term toxicity testing methods, improved mixture characterization, understanding the fate and bioavailability of PAH mixtures, and understanding exposure route-related differences in carcinogenicity are discussed as ways to improve the understanding of the risks of PAHs.