If axion Dark Matter exist, then they can collapse to form self-gravitating exotic compact objects known as axion stars. As mergers of such compact objects can potentially yield detectable gravititational waves, much effort have been expended to compute these signals. I will discuss both the technical and theoretical challenges of this endeavour. In particular, I will show that axion stars may not be stable to electromagnetic decay, raising the question on whether we should expect to see these objects in the first place