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Axions and axion-like particles are excellent dark matter candidates, spanning a vast range of mass scales from the milli- and micro-eV for the QCD axion, to 10^-22eV for ultralight axions, to even lighter candidates that make up the “axiverse”. In some scenarios, inhomogeneities in the axion density lead to the formation of compact structures known as axion “miniclusters” and axion stars. I will first discuss astrophysical and cosmological constraints on axions at either end of this spectrum, using data from the cosmic microwave background anisotropies and the effects of miniclusters on the gravitational microlensing and on direct detection. I will then assess novel techniques for axion radioastronomy involving miniclusters. The last part will be devoted to assessing the spectrum of primordial gravitational waves from axion strings, that could possibly be detected in future experiments.