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The infrared spectra of many galactic and extragalactic objects are dominated by emission features at 3.3, 6.2, 7.7, 8.6 and 11.2 \mu m. The carriers of these features remained a mystery for almost a decade, hence the bands were dubbed the unidentified infrared (UIR) bands. Since the mid-80's, the UIR bands are generally attributed to the IR fluorescence of Polycyclic Aromatic Hydrocarbon molecules (PAHs) upon absorption of UV photons -- the PAH hypothesis. Here we review the progress made overdoi:10.1017/s174392131102494x fatcat:k7vte4mekzayhf4gdyvrnuljj4