Abstract. In the long story of interstellar PAHs, computations have played and are still playing a fundamental role in connection with experiments and observations. From the very first calculations of the IR spectra of small PAHs in the late eighties to the more recent ones, every aspect of the research linked to the PAH hypothesis has evolved dramatically: the size and the variety of the molecules considered, the techniques used, the precision of the astronomical observations . . . The initial landscape has completely changed though the quest is still the same, that is to correlate the so-called UIR bands spectra ubiquitous in the ISM (Inter Stellar Medium) with a chemical family of molecules, the PAHs. An historical review of the 25 years of this quest is presented here, focusing on the computational part.