Octopuses are highly intelligent, possibly more so than any other order of invertebrates. The exact extent of their intelligence and learning capability is much debated among biologists, but maze and problem-solving experiments have shown evidence of a memory system that can store both short- and long-term memory. It is not known precisely what contribution learning makes to adult octopus behavior. Young octopuses learn almost no behaviors from their parents, with whom they have very little contact.
The octopus has a highly complex nervous system, only part of which is localized in its brain. Two-thirds of an octopus's neurons are found in the nerve cords of its arms, which have limited functional autonomy. Octopus arms show a variety of complex reflex actions that persist even when they have no input from the brain. Unlike vertebrates, the complex motor skills of octopuses are not organized in their brain using an internal somatotopic map of its body, instead using a nonsomatotopic system unique to large-brained invertebrates. Despite this delegation of control, octopus arms do not become tangled or stuck to each other because the suction cups have chemical sensors that recognize octopus skin and prevent self-attachment. Some octopuses, such as the mimic octopus, will move their arms in ways that emulate the shape and movements of other sea creatures.

In laboratory experiments, octopuses can be readily trained to distinguish between different shapes and patterns. They have been reported to practice observational learning, although the validity of these findings is widely contested on a number of grounds. Octopuses have also been observed in what some have described as play: repeatedly releasing bottles or toys into a circular current in their aquariums and then catching them. Octopuses often break out of their aquariums and sometimes into others in search of food. They have even boarded fishing boats and opened holds to eat crabs.