One of the great pleasures of having a canine companion is watching them fall into an exhausted pile of fur after a long day of doing absolutely nothing. It’s at this point that many pet owners wonder: What do dogs dream about, if they dream at all?

First, researchers believe that yes, dogs do dream. There’s no actual testimony, but we know from a 2001 MIT study with rats that the animals can enter REM sleep and exhibit the same brain activity as they did while they were navigating a maze earlier. Other studies using electroencephalogram (EEG) devices have been able to observe similar activity in dog brains while slumbering. Like humans, dogs have a sleep stage where their breathing slows and their eye movements become rapid—all indicators that dreaming could occur.

There’s also the superficial evidence: Dogs often bark or twitch while asleep in ways that imply they’re dreaming of chasing an elusive target. (Or leaf.)

That’s because dogs, like us, probably dream about the events of the day—in their case, running, jumping, or playing. Dreams can even be breed-specific, as in the case of Pointers that go “on point” as though they were spotting game. Smaller dogs also tend to dream more than larger dogs, and older dogs more than midlife dogs.

Details of those dreams remain elusive. Apart from physical clues, it’s hard to know exactly what goes through an animal’s mind. Some gorillas who have been taught sign language have communicated their dreams to their handlers—sometimes about people they’ve seen recently. It’s also possible dogs dream about their owners frequently, since the canine/human bond is so strong.

If you want to observe dreaming in your own dog, experts recommend you wait until about 20 minutes after they’ve dozed off. Their muscles may begin to twitch and their eyes might start to flutter, both likely signs the dog is entering REM and starting to dream. It’s also important not to disturb them during this stage of sleep, since it can be startling to them. If you leave them be, maybe they’ll finally have an opportunity to catch whatever they’ve been chasing.

So what do dogs dream about? A lot of the time, probably the thing that’s most often on their mind: you.

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