The myelin sheath, and hence the myelin-forming cells (i.e. Schwann cells in the PNS and oligodendrocytes in the CNS), have been a crucial acquisition of vertebrates. The major function of myelin is to increase the velocity of propagation of nerve impulses. Invertebrate axons are ensheathed by glial cells, but do not have a compact myelin. As a consequence, action potentials along invertebrate axons propagate at about 1 m/s, or less. This is sufficient, however, for the survival of small animals (between 0.1 and 30cm). Among invertebrates, only the cephalopods are larger. By increasing their axonal diameter to 1 mm or more, cephalopods have been able to increase the speed of propagation of action potentials and therefore adapt nerve conduction to their larger body size. However, due to the physical constraint imposed by the skull and vertebrae, vertebrates had to find an alternative solution. This was achieved by introducing the myelin sheath, which leads action potentials to propagate at speeds of 50-100m/s without increasing the diameter of their axons. Not all vertebrate axons, however, are myelinated. In the protovertebrates (lancelets, hagfishes, lampreys), which belong to the agnathes (jawless fishes), axons are not ensheathed by myelin. Among living vertebrates, the most ancient myelinated species are the cartilaginous fishes (sharks, rays), suggesting that acquisition of myelin is concomitant with the acquisition of a hinged-jaw, i.e. the gnathostoma. The close association between the apparition of a hinged-jaw and the myelin sheath has led to speculation that among the devonian fishes that have disappeared today, the jawless conodonts and ostracoderms were not myelinated, and that myelin was first acquired by the oldest gnathostomes: the placoderms. I also question where myelin first appeared: the PNS, the CNS or both? I provide evidence that, in fact, it is not the type of myelin-forming cell that is crucial, but the appearance of axonal signals, rendering axons receptive to inducing an ensheathing glial cell to wrap around the axon. Under certain circumstances or in some species, invertebrate ensheathing glial cells wrap around axon to form a pseudo-myelin sheath. Therefore, to form myelin it was not compulsory to 'invent' a new cell type. Hence my conclusion that myelination has most probably started simultaneously in the PNS and the CNS, using pre-existing ensheathing glial cells.