In many ways, the octopus is as close to alien life as we may ever see. Few creatures in the world are as remarkable and bizarre. A part of a class of animals called cephalopods, they are among the most intelligent and most mobile of all the invertebrates. They live in every ocean in the world, in the deep sea, in kelp forests, in coral reefs, along rocky shorelines. And they are as diverse as the habitats they live in. They can be massive, or absolutely tiny. Some species are venomous, and some are just downright strange. In any given moment, they can appear spikey, or they can appear smooth. They are so different from us, that most of their 500 million neurons are not in their brain, but in their arms, which can smell and taste, and even think. And so intelligent that their cognitive ability matches that of many large-brained vertebrates. They have left scientists stunned about how a creature so far from us on the evolutionary tree could evolve such complex behaviors, their intelligence emerging in an entirely novel and independent way from our own. So how did the octopus become so biologically complicated – an island of complexity in the sea of invertebrate animals? Just how intelligent are they, and how can studying them reveal information about our own minds?