SummaryThe advances in the knowledge of the histology of the central nervous system which have been made possible by improved staining techniques have complicated and confused the anatomical conception of the perivascular and perineuronal spaces. As a first step towards the resolution of this confusion, a clear picture must be formed of the elements which intervene between the tunica media of the cerebral and spinal blood vessels and the neurons.The blood vessels in the central nervous system possess little or no adventitial coat, and this element is replaced by a reticular perivascular sheath continuous with the pia‐arachnoid envelope of the brain and spinal cord. The question as to whether this reticular sheath extends to cover the capillaries remains to some extent unanswered, though the probability is that it does not do so. No clearly defined tissue layer serves to separate the outer wall of the reticular perivascular sheath from the neuron and its processes. In fixed preparations a felted network, formed by the perivascular feet of the neuroglia, which resembles a membrane, is seen, but we do not accept the view that this structure is part of the normal anatomy of the central nervous system. There remains an element on which little stress has previously been laid: this is the ground substance of the central nervous system, a tissue which is probably a muco‐polysaccharide in constitution, and which by virtue of its physical and chemical properties may well be of considerable importance in relation to the physiology of the central nervous system.The views of the earlier authorities on the anatomy of the perivascular and perineuronal spaces are difficult to reconcile with modern knowledge of the histology of the tissues concerned, and are of interest chiefly because of the influence which they have had on descriptions of these structures which are still accepted to‐day. After the first description of the perivascular space by Pestalozzi, important landmarks in the subsequent history of the spaces were: the adoption of the term ‘Virchow‐Robin space’ for the perivascular space; the description by His of a second space external to this; the discovery by Obersteiner that the perineuronal spaces were continuous with the space of His, and the confusion by later workers of the space of His with that of Virchow‐Robin, so that the perineuronal spaces were described as communicating through a perivascular canalicular system with the subarachnoid space.The most influential figure in moulding the modern conception of the perivascular and perineuronal spaces has been Weed. It appears that he accepted the notion, prevailing at the time at which his researches were carried out, of a complete canalicular system of spaces opening into the subarachnoid space; and it was unfortunate that the limitations of his Prussian blue technique were such as to lead him to support this misconception.Schaltenbrand & Bailey and Patek did much to resolve the confusion produced by the existence of the two systems of spaces, the true perivascular space of Virchow‐Robin and the artifact space of His or Held. Schaltenbrand & Bailey regarded the combined outer wall of the reticular perivascular sheath and glial membrane (their ‘Piaglialmembran’) as separating the two systems of spaces. Patek, who used an improved version of Wee?s technique, described one true perivascular space, the Virchow‐Robin space, with which the perineuronal spaces did not communicate, and three artifact spaces, with one of which, that between the glial membrane and the brain substance, the perineuronal spaces were in communication.The consideration of the views of previous workers, taken in conjunction with our own observations, leads us to believe that there are two systems of perivascular spaces: (1) the true perivascular spaces bounded by the layers of the reticular perivascular sheath; and (2) a great system of artifact spaces produced by shrinkage in the preparation of histological material and extending from the perineuronal spaces through the artifact perivascular spaces to the epispinal spaces of His.Such a conception of the histology of the perivascular and perineuronal spaces must, if accepted, alter some modern views on certain problems in connexion with the anatomy and physiology of the central nervous system. We suggest that the perivascular spaces serve neither for the production nor the absorption of the cerebro‐spinal fluid, but, being channels in which there is no established flow in one direction, act as cushions between the expansile vessels and the nerve cells. We also believe that our investigations show that the anatomical arrangements are such that the perivascular channels can play no significant part in the metabolism of the neuron.Whilst the perivascular and perineuronal spaces have in all probability little relevance to the problems of the blood‐brain barrier and the anatomy of the synapse, it is evident that the importance of the ground substance in relation to these problems has not been adequately appreciated.