The evolution of the nervous system emerged in primaeval animals to coordinate their behaviour then advanced by the division of function between neurones and neuroglia; neurones became dedicated to information processing and neuroglia specialised in homeostatic support. As the nervous system became more complex and neurones extended axonal connections, so periaxonal glial cells arose to provide axonal support. In many invertebrates, periaxonal glia produce multilamellar structures similar in architecture and function to the myelin sheath of vertebrates. These protomyelin structures support exceptionally high velocity of action potential propagation, which in some shrimps may reach 200 m/s. Myelin sheaths ‘proper’ are a vertebrate development and emerged in jawed fish with the central nervous system (CNS) of the brain and spinal cord becoming enclosed within the cranium and vertebral column. This was coincident with a clear division between oligodendrocytes that myelinate axons in the CNS and Schwann cells that myelinate peripheral axons; it seems likely that peripheral myelin evolved first. In the CNS, myelinated axons form the white matter, which interconnects the different regions of the CNS with each other and with the periphery. This is termed the connectome, which is particularly advanced in humans, occupying ~50% of total volume of the brain, compared to ~12% in rodents. The highly developed connectome, supported by oligodendroglial cells, is the foundation of human intelligence.