Light bosonic fields may suffer an instability around a rotating compact object. This process, known as superradiance, leads to the exponential amplification of the field around a black hole or neutron star, while the spin of the central object is correspondingly depleted. The discovery of a highly spinning black hole could therefore be used to constrain the existence of light bosons such as axions in a particular range of masses. These constraints apply for very low non-gravitational couplings between the boson and the Standard Model, offering a powerful search strategy for new physics. However, care must be taken to include the more complex effects of the black hole's astrophysical environment. Conversely, stellar superradiance could allow us to probe additional non-gravitational interactions between a new boson at the stellar matter. In this article, I will discuss the current status and future directions of axion superradiance.