I will describe a large ensemble of compactifications of type IIB string theory on Calabi-Yau threefold hypersurfaces, obtained by triangulating polytopes from the Kreuzer-Skarke list. We have developed methods to compute effective theories in the previously-inaccessible region with many Kahler moduli that plausibly contains almost all vacua in this class. We find that ultralight axions are ubiquitous when the sigma model expansion is under control. I will comment on work in progress examining the implications for axion inflation, axion dark matter, and astrophysical and cosmological axion searches. Finally, I will describe a related issue concerning the axion potential from non-BPS Euclidean D3-branes wrapping non-effective divisors, and will link this to geometric measure theory and the Weak Gravity Conjecture.