Strong emission features dominate the IR spectra of the interstellar medium of the Milky Way, galaxies in the local Universe and out to redshifts of ~3. These features are generally attributed to IR fluorescence of large Polycyclic Aromatic Hydrocarbon (PAH) molecules pumped by UV photons. These species must be abundant, ubiquitous, and an important component of the ISM. However, despite extensive experimental and theoretical efforts, no specific PAH or even classes of PAHs have been unambiguously identified. Hence, we do not really know the intrinsic physical and chemical properties of these species and therefore cannot quantify their role in the Universe. I propose a highly interdisciplinary program combining observational, theoretical, and experimental studies to determine the IR emission characteristics of large PAH molecules, their origin and evolution, and their influence on the Universe around us. The proposed program will analyze interstellar PAH spectral maps obtained with Spitzer and ISO and relate the spatial variations in the spectral diversity to variations in the characteristics of the radiation field and the physical conditions of these regions that will be obtained with Herschel. This observational program will be aided by an innovative laboratory program that will measure the IR characteristics of large, astrophysically relevant PAH molecules in the gas phase and by a modelling program of the emission characteristics of these PAHs in space. In addition, the photochemistry of gaseous PAHs will be studied in the laboratory using novel techniques, allowing us to model the chemical evolution of PAHs and their reaction products in the interstellar medium. In this way, key astronomical questions involving interstellar PAHs can be addressed.