  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 over the past 25 years in
understanding the UIR bands and their carriers.
