The octopus and its close relatives the cuttlefish and squid are the most advanced of the invertebrates, possessing the largest brains both in weight and cell numbers. Here I review recent studies of the neurophysiological properties of the vertical lobe system (VL) in the cephalopod brain, a system already thought to be dedicated to learning and memory. Summarizing from the point of view of comparative evolution, I relate these results to other systems where anatomical and electrophysiological data are available, mainly the insect mushroom bodies and the mammalian hippocampus. The emerging results suggest that a convergent evolutionary process has resulted in similar neural organization and activity-dependent long-term synaptic plasticity in all these learning and memory systems, even though the invertebrate systems conserve their typical anatomical and electrophysiological features. And finally, functional inferences based on the comparison with the insect mushroom.