In this talk we consider 4d N=1 compactifications of IIB superstring theory on Calabi-Yau (CY) orientifolds. We study the effective field theory of axions arising from the dimensional reduction of the C4 Ramond-Ramond form on holomorphic 4-cycles. We determine the spectrum of these axions for all Calabi-Yau manifolds belonging to the Kreuzer-Skarke database, for hodge numbers 2<h11<7. We compute masses and decay constants of such axions, as a function of the vacuum expectation value of Kahler moduli. We compare our results with cosmological and astrophysical bounds for dark matter abundance. In particular, we establish the possibility that axion dark matter in these models could be realized by fuzzy axions, with a misalignment production mechanism. We further comment about the peculiar role that the QCD axion plays in this set of models, as well as comments about the generic presence of an additional dark photon sector.