The quantum chromodynamics axion is a well-motivated dark matter candidate that may also solve the strong CP problem related to the absence of the neutron electric dipole moment. Multiple experimental efforts are currently racing to try to discover this particle in the laboratory. In this talk I will show that astrophysical observations are also a promising path towards detecting the axion. In particular, I will demonstrate that axion dark matter may convert to narrow radio lines in the strong magnetic fields surrounding neutron stars. I will present first results from a dedicated radio search performed with data from the Green Bank and Effelsberg radio telescopes, and I will discuss future detection prospects.