The QCD axion, originally proposed to resolve the ‘so-called strong CP problem’, has emerged in recent years as one of the most compelling dark matter candidates. Arguably the most promising strategy to indirectly search for the existence of axion dark matter involves using radio telescopes to look for axion-photon conversion deep in the magnetospheres of neutron stars. Unfortunately, many theoretical and modeling uncertainties have prevented this approach from being seen as fully robust. In this talk, I will discuss recent (and on-going) theoretical and computational developments that are allowing us for the first time to meaningfully characterize the expected radio signature and manage the aforementioned uncertainties. I will also discuss a novel approach for generating axions directly in the magnetosphere itself from the collapse of vacuum gaps, a process which may generate a highly complementary radio signature from that of the local axion dark matter.