Metrics & MoreArticle Recommendations CONSPECTUS: Polycyclic aromatic hydrocarbon molecules (PAHs) are ubiquitously present at high abundances in the Universe. They are detected through their infrared (IR) fluorescence UV pumped by nearby massive stars. Hence, their infrared emission is used to determine the star formation rate in galaxies, one of the key indicators for understanding the evolution of galaxies. Together with fullerenes, PAHs are the largest molecules found in space. They significantly partake in a variety of physical and chemical processes in space, influencing star and planet formation as well as galaxy evolution.Since the IR features from PAHs originate from chemical bonds involving only nearest neighbor atoms, they have only a weak dependence on the size and structure of the molecule, and it is therefore not possible to identify the individual PAH molecules that make up the cosmic PAH family. This strongly hampers the interpretation of their astronomical fingerprints. Despite the lack of identification, constraints can be set on the characteristics of the cosmic PAH family thanks to a joint effort of astronomers, physicists, and chemists. This Account presents the spectroscopic properties of the cosmic PAH emission as well as the intrinsic spectroscopic properties of PAHs and astronomical modeling of the PAH evolution required for the interpretation of the cosmic PAH characteristics. We discuss the observed spectral signatures tracing PAH properties such as charge, size, and structure and highlight the related challenges. We discuss the recent success of anharmonic calculations of PAH infrared absorption and emission spectra and outline the path forward. Finally, we illustrate the importance of models on PAH processing for the interpretation of the astronomical data in terms of the charge balance and PAH destruction. Throughout this Account, we emphasize that huge progress is on the horizon on the astronomical front. Indeed, the world is eagerly awaiting the launch of the James Webb Space Telescope (JWST). With its incredible improvement in spatial resolution, combined with its complete spectral coverage of the PAH infrared emission bands at medium spectral resolution and superb sensitivity, the JWST will revolutionize PAH research. Previous observations could only present spectra averaged over regions with vastly different properties, thus greatly confusing their interpretation. The amazing spatial resolution of JWST will disentangle these different regions. This will allow us to quantify precisely how PAHs are modified by the physical conditions of their host environment and thus trace how PAHs evolve across space. However, this will only be achieved when the necessary (and still missing) fundamental properties of PAHs, outlined in this Account, are known. We strongly encourage you to join this effort.