Axions are intriguing candidates for dark matter. Depending on the formation mechanism of axion dark matter, the axion field may exhibit large density fluctuations on small scales. These density fluctuations lead to the formation of self-gravitating clumps of axions, known as miniclusters and axion stars. In this talk, I will discuss these clumps, what is, and what is not, known about them, and how to, perhaps, find them. In one of the classical axion dark matter scenarios (where the Peccei-Quinn symmetry is broken after the end of inflation), most of the axion dark matter may be bound in such axion clumps. On the one hand, this makes "direct detection" type searches for axions such as ADMX more difficult, since the ambient axion density might be much lower than the usual ~0.3 GeV/cm^3 expectation. On the other hand, such axion clumps might offer new exciting possibilities for "indirect detection" of axions: if such an axion clump encounters a neutron star, the axions could resonantly convert into radiophotons in the neutron star's magnetosphere. The signal would be a narrow spectral line, strongly anisotropic, and lasting a typical time scale of ~1 year for an axion minicluster to ~1 minute for an axion star.