The cold dark matter (CDM) problem is one of the important unsolved problems in cosmology today. The axion is one of the well motivated CDM candidates whose weak spontaneous decay to photons is enhanced in the presence of magnetic fields. This thesis examines the prospects of detecting the axion-photon decay in astrophysical magnetic fields using radio telescopes, with special reference to cosmological objects and neutron stars. Cosmological objects are found to be ill- suited to the detection of the enhanced decay because of the large scale structure of magnetic fields in such objects. However, nearby massive galaxy clusters might offer a chance of detection of the spontaneous decay, although this requires a clear understanding of the density profile of such clusters. Neutron stars and their magnetospheres are home to a resonance effect that could be one of the best chances of detection in future searches. We develop a general formalism that allows us to determine the different assumptions that lead to different results in the literature. We also examine the detectability of the flux from this resonant decay and find that radio telescopes are sensitive enough to probe the regions of CDM axion parameter space hitherto unexplored.