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^(-22)eV for ultralight axions that make up the "axiverse". In some scenarios, the collapse of the non-homogeneous axion field leads to the formation of two kind 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 anticipate some work in progress at GRAPPA on the new branch of "axion radio-astronomy" that involves neutron stars and axions. I will then assess the formation and the evolution of axion stars in various astrophysical regimes.