I can't answer your question about current research, but here are a couple of older references. In 1986 a linguistics grad student, Esmé Hoban, at the University of Hawaii spent time observing experiments on dolphin-human communication experiments done at Lou Herman's Kewalo Basin lab. She did her dissertation on this and on broader concerns, The promise of animal language research. She thought the experiments that she observed had severe methodological problems. I was on her dissertation committee, and her chairman was Derek Bickerton, who himself wrote about the general topic in, among other books, Language and Species.
Derek also wrote a novel, King of the Sea, which speculates about what dolphin language would be like, if there were a dolphin language. (Derek also takes up the matter of human-dolphin sexual communication, in the novel.)