The past few years have seen major advances in understanding the properties of axions in string theory. This progress is thanks to new computational tools that allow for fast and automated calculations with Calabi-Yau manifolds. I will describe the predictions string theory makes for axion masses, decay constants, and axion-photon couplings, and how these depend precisely on the topology of the Calabi-Yau. I will describe explicit constructions of millions of axiverse models on Calabi-Yaus with Hodge numbers up to 491, across the whole Kreuzer-Skarke database (and some results beyond this). Phenomenology computed includes: black hole superradiance, dark matter relic density, fuzzy dark matter, decaying heavy relics and the intergalactic medium, and the QCD axion mass. I will describe the correlation between QCD axion mass and topology, and how this makes it possible for axion "haloscope" experiments to experimentally infer Hodge numbers, divisor topologies, and moduli space loci. I demonstrate the statistical state of the art by computing a full forward model incorporating likelihoods from the cosmic microwave background and Lyman-alpha forest and find the maximum Bayesian posterior probability region on the moduli space of a given CY favoured by a resolution of the tension in these data by an ultralight axion composing 1% of the dark matter.