In this talk I will discuss a variety of ideas centered on how extreme compact objects (specifically, neutron stars and black holes) can efficiently produce and confine axions, allowing one to achieve enormous densities and field gradients that can help to offset the intrisically feeble nature of the axion coupling. I will start by discussing the well-known example of black hole superradiance, in which light axions can rapidly extract the rotational energy of black holes, in the process populating quasi-bound states with energy densities exceeding the background dark matter density by more than 35 orders of magnitude. I will then discuss a distinct, but somewhat analogous, process occuring around neutron stars, whereby axions can indirectly siphon rotational energy via a coupling to the electromagnetic fields, once again accumulating on large timescales and producing high-density environments capable of generating striking observational signatures. Finally, I will discuss how static axion configurations can be sourced from the dense nuclear matter inside neutron stars, and how the spatial gradients of these field configurations can influence the electromagnetic emission of these objects.
