I'd like to point out the slides of the talk: All Your Baseband Are Belong To Us by Ralf-Philipp Weinmann.
Ralf is one of those few people on this planet who have understood the security implications of now being able to send arbitrary protocol frames (particularly GSM L3 04.08 frames) to mobile phones.
GSM protocol stacks have never been written with the assumption that somebody might send intentionally malformatted messages on the air interface. But at the same time, the GSM network does not authenticate itself to the phone, i.e. everyone who can present a network-side GSM air interface to a phone will be able to exchange arbitrary messages with the phones.
This problem has been outlined in all the GSM security workshops and presentations I have been giving during recent years. Still, apart from Ralf-Philipp Weinmann's work, I have not seen a lot of public research in that area.
Exploiting and owning the baseband processor is a dangerous threat, as the microphone and entire audio path are connected to that very processor. Whoever owns the baseband can turn the mobile phone into a passive surveillance device, commonly called 'bug'. Since application processor and baseband processor are very far apart these days, with various layers of software in between, the user interface will not show any indication of what the baseband processor does.