Yes, all signs point to dogs dreaming: during their rapid eye movement sleep, we observe rapid eye movements, twitching of the paws, twitching of the lips, and sometimes small yaps—signs of intense brain activity comparable to that of wakefulness.
What the sleeping brain reveals
A dog's sleep alternates between slow-wave and REM phases, the latter accounting for roughly 10 to 12 percent of total sleep time. During these episodes, which typically last a few minutes, the cortex and brainstem become active much as they do when awake, while the body remains largely paralyzed—a mechanism called muscle atonia. In dogs, this atonia is often incomplete, which explains the visible movements of the paws, tail, or nose.
The strongest evidence about what happens during these episodes comes from rat studies: by recording hippocampal neuron activity during REM sleep, researchers showed that sequences observed while running through a maze while awake replayed in the same order during the sleep that followed. This "replay" phenomenon is thought to be a mechanism for consolidating spatial memory. We don't have equivalent recordings in dogs, but their brain architecture and REM sleep organization are similar enough to rats and other mammals that cautious extrapolation is reasonable: the twitching observed could correspond to a replay of actions experienced during the day, such as running or sniffing, though we cannot say whether the dog has a subjective experience comparable to human dreaming.
Why you shouldn't wake a dog during this phase
A dog pulled abruptly from REM sleep may react in a disoriented or even aggressive way as a defensive reflex, because the brain needs a moment to resynchronize perception and movement. It is therefore best to let it complete its sleep cycle naturally. If twitching is accompanied by violent movements, stiffness, or abnormally prolonged vocalizations outside of sleep, veterinary advice allows you to rule out a neurological cause.