The particle that makes up the dark matter of the universe could be an axion or some other light boson. A collection of axions can condense into a gravitationally bound Bose-Einstein condensate called an axion star. It is possible that a significant fraction of the axion dark matter is in the form of axion stars. This would make some efforts to identify the axion as the dark matter particle more challenging, but it would also open up new possibilities. I will summarize the basic properties of axion stars and other gravitationally bound or self-bound condensates of spin-0 particles. Axions are naturally described by a relativistic field theory with a real scalar field, but low-energy axions can be described more simply by a classical nonrelativistic effective field theory with a complex scalar field.
