Abstract The available literature on neurological disorders reported in the context of the current COVID-19 pandemic documents an array of manifestations affecting the central nervous system (CNS), the peripheral nervous system (PNS) and muscle. These are based on case reports and small number series mainly from Wuhan, northern Italy and New York. A dearth of knowledge exists in the understanding of whether the neurological manifestations are caused by or merely associations with COVID-19 infection. CNS involvement is observed more commonly, and includes headache, decreased level of consciousness, seizures, encephalopathy and disturbance of smell and taste. The latter has emerged as a prominent often early symptom and is considered an indicator of the neurotropic properties of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The profound and often times fatal respiratory failure associated with severe COVID-19 possibly has a neurogenic component with involvement of respiratory brainstem nuclei as a result of transneural viral spread from olfactory or bronchopulmonary receptor nerve endings progressing to the medullary respiratory centres. A generalised endotheliitis and prothrombotic inflammatory state leads to cerebrovascular complications with ischaemic strokes (often large vessel), intracerebral haemorrhage and occasionally cerebral venous thrombosis. Acute haemorrhagic necrotising encephalopathy has been described as a neurological manifestation of the cytokine storm. Postinfectious myelitis has been documented. The PNS involvement includes cases of Guillain–Barré syndrome and some of its variants or formes frustes; myositis of varying degree and severity is encountered. Direct viral neurotropic disorders need to be distinguished from secondary neurological disease resulting from systemic multi-organ illness and from mere coincidental co-occurrence of COVID-19 and a neurological condition. Future clinicopathological studies will need to clarify some of these questions.