For pulses or bursts of emission, we like compact objects, just from light-travel-time arguments. I would say that the leading models involve very young, highly

For pulses or bursts of emission, we like compact objects, just from light-travel-time arguments. I would say that the leading models involve very young, highly magnetic neutron stars ("magnetars"), either embedded in their birth supernova remnants / wind nebulae, or in the environments of massive black holes (as in the center of our Galaxy). There are good reasons for these specific models to be favored. But honestly, we don't know for sure yet. Could it be cosmic strings? Evaporating microscopic black holes? Blobs of gas being flash-annihilated by drifting into the beams of active galactic nuclei? Theorists have models that seem to be OK on paper, and we're working hard to kill their models with new observations. (One thing I'll say - and I say this as a firm optimist about the prospect for aliens - this is NOT aliens.)