Despite decades of research on per- and polyfluoroalkyl substances (PFAS), fundamental obstacles remain to addressing worldwide contamination by these chemicals and their associated impacts on environmental quality and health. Here, we propose six urgent questions relevant to science, technology, and policy that must be tackled to address the “PFAS problem”: (1) What are the global production volumes of PFAS, and where are PFAS used? (2) Where are the unknown PFAS hotspots in the environment? (3) How can we make measuring PFAS globally accessible? (4) How can we safely manage PFAS-containing waste? (5) How do we understand and describe the health effects of PFAS exposure? (6) Who pays the costs of PFAS contamination? The importance of each question and barriers to progress are briefly described, and several potential paths forward are proposed. Given the diversity of PFAS and their uses, the extreme persistence of most PFAS, the striking ongoing lack of fundamental information, and the inequity of the health and environmental impacts from PFAS contamination, there is a need for scientific and regulatory communities to work together, with cooperation from PFAS-related industries, to fill in critical data gaps and protect human health and the environment.