Comparative analysis of brain function in invertebrates with sophisticated behaviors, such as the octopus, may advance our understanding of the evolution of the neural processes that mediate complex behaviors. Until the last few years, this approach was infeasible due to the lack of neurophysiological tools for testing the neural circuits mediating learning and memory in the brains of octopus and other cephalopods. Now, for the first time, the adaptation of modern neurophysiological methods to the study of the central nervous system of the octopus allows this avenue of research. The emerging results suggest that a convergent evolutionary process has led to the selection of vertebrate-like neural organization and activity-dependent long-term synaptic plasticity. As octopuses and vertebrates are very remote phylogenetically, this convergence suggests the importance of the shared properties for the mediation of learning and memory.