I've written a number of essays about grief in nonhuman animals (animals), the latest called "How Animals Grieve: Saying Goodbye to Family and Friends." I've always argued that it's really a matter of how animals grieve, not if they grieve. This is an important distinction because the essential question is why grief has evolved - not if it has evolved. This line of thinking applies to studies of animal emotions in general.
I just learned about a heart wrenching video of an adult dog discovering the corpse of a puppy and burying the youngster in a highly ritualized manner, resembling a sequence of behavior that I've observed in red foxes as a female buried a male who was most likely her mate. I was fascinated for she was deliberately orientingt her body so that when she kicked debris with her hind legs it would cover the corpse. She'd kick dirt, stop, look at the carcass, and intentionally kick again. I observed this ritual for a short while. The dog in this video goes through the same sequences of behavior for about three minutes and only leaves after the corpse is completely covered.