Neurological complications have emerged as a significant cause of morbidity and mortality in the ongoing COVID-19 pandemic. Beside respiratory insufficiency, many hospitalized patients exhibit neurological manifestations ranging from headache and loss of smell, to confusion and disabling strokes. COVID-19 is also anticipated to take a toll on the nervous system in the long term. Here, we will provide a critical appraisal of the potential for neurotropism and mechanisms of neuropathogenesis of SARS-CoV-2 as they relate to the acute and chronic neurological consequences of the infection. Finally, we will examine potential avenues for future research and therapeutic development.