Classified as cephalopods, which means "head-foot" in Greek, octopi are quite different from their snail, slug, clam, and oyster cephalopod peers. While a common pond snail has approximately 10,000 nuerons, octopi such as the common octopus, about which the most research has been studied, have approximately 500 million neurons. Compmare that to the most nueronally complex invertebrates up to them - cockroaches and honeybees: those species only reach up to about one million nuerons. So for an invertebrate, octopi are on a whole other level. So much so that scientists are continually questioning and testing octopi intelligence, trying to determine how "smart" they really are.
But remember, octopi don't have a spinal cord (no bones make for great hiding and shape morphing abilities) that acts as a lifeline for the neurons to the body like we do. Instead 35% of their neurons are in their brain, which handles higher executive functions such as decision-making, learning, memory, and coordination of complex movements. Meanwhile, the rest of their neurons live in their arms! Each of an octopus's eight arms has interlinked control centers called ganglia that relay information to the brain and also independently control movements such as extending or twisting.
Now wait - it gets even cooler. Each arm has 200 to 300 suckers which are not only extremely tactile sensitive (and can individually grasp and twist), but also have taste receptors - meaning they can taste with their arms! This is actually how they do most of their hunting, and due to the fact that each arm has so many neurons itself, even when an arm is severed from an octopus's body, it can continue to hunt on its own, functioning as an independent body, and upon capturing a prey will search to bring the food to it's non-existent body's mouth.
Learn even more nifty facts - about their changing skin color and texture, crazy octopus sex positions, and get-away inking tactics from the video!