When chimps play, Panksepp notes, they make panting sounds that could be a form of laughter. Even rats have a way of laughing--by chirping when they're playing with each other or being tickled by humans.
But, if animals do in fact laugh, what are they laughing at? Scientists have long known that for many animals, life isn't all about hunting, foraging, fighting, and sleeping. Young animals also play a lot, which suggests that animal laughter is related to playful joy.
How is this possible? Human laughter originates in very ancient areas of the brain. This suggests that mammalian brains were wired for playful joy long before the rise of modern humans. So it's not too much of a stretch to claim that pre-human forms of laughter may exist.
To be clear, it's not certain that animals really laugh like humans, at least not in response to humor. However, many studies suggest that animals are capable of complex emotions such as fear, anger, and even joy and sadness.
So your dog's grin may not be a real human-type smile. But it now seems likely that deep in brain regions that animals share with humans, the ability for joy and ancients forms of laughter do exist.