Watching one of those animal planet shows about extraordinary animals. Yes, I know, doesn't narrow it down much. The nursing home dog who knew when people were going to die. The animal psychic with all her cockeyed confidence, made me want to throw something at her. The more scientific approach of the animal behaviorist who was sure it was a scent given off didn't impress me terribly either. Not that the latter is necessarily wrong, so much as the explanation isn't based on any real evidence. Just as much a guess as the psychic, however much given with hedging.
I've worked with the dying. I'm sure something happens when someone dies. As hospice nurses on a floor, we knew when to start watching, and knew when the aide called to us it was because of death. Just as people know when they get the call, and don't need to be told the actual words "she's dead." When I had to call a family, I never had to be more specific, only giving the time- if anything. Odd circumstances happened nearly every time, often not obviously related.
I will not try to guess the mechanism. But the best anecdotes of non-local communication seem to be very real crises, with strong emotional components, between people with a bond. Which is why putting it in a lab cannot recreate the circumstances. Not ethically, anyway. Because it inherently cannot be real peril, is not done with people closely attached, and getting the emotional circumstances right is no end of tricky. Not to mention that the response, the message as received, is not quantifiable. Proof isn't going to come in a neat package.
As for what a dog senses? Problematic.
I do think we are capable of more than just the obvious senses, but I' not about to go all wooo wooo! about it. It's not magical, it's just difficult to qualify. The damned data isn't all hoax, not all foolishness. The exceptions have often been the keys to unlocking understanding. The abnormal informs the normal.