Dogs dream during the REM phase of sleep, just like humans. There is evidence that they dream about their daily activities. They often twitch, vocalize and breathe differently while dreaming.
According to Dr. Stanley Coren, canine brains are similar in structure to human brains and they probably have similar dreams. Scientists have studied canine dreams by watching the electrical activity of their brains as they sleep. In one study, scientists blocked the portion of the brain that keeps dogs from moving around during sleep. They observed that the dogs acted out routine activities, such as hunting or playing, despite being fast asleep.
Scientific studies on rats further support these conclusions. Rats have a less advanced brain structure than dogs but are believed to have very detailed dreams. Scientists studied the electrical activity of the rats' brains after they had navigated a maze earlier in the day. The researchers discovered that the electrical activity of a sleeping rat's brain was very similar to its brainwaves while running the mazes. Since this has been so clearly proven in rats, it is safe to conclude that dogs dream as well.
Like humans, dogs have to reach a deep stage of sleep before dreaming. This usually takes about 20 minutes from the time the dog falls asleep. Dogs may not always show easily observable signs that they are dreaming, but under close examination, it is possible to see their eyes moving rapidly.