COVID-19 is a highly infectious viral disease caused by the novel coronavirus SARS-CoV-2. While it was initially regarded as a strictly respiratory illness, the impact of COVID-19 on multiple organs is increasingly recognized. The brain is among the targets of COVID-19, and it can be impacted in multiple ways, both directly and indirectly. Direct brain infection by SARS-CoV-2 may occur via axonal transport via the olfactory nerve, eventually infecting the olfactory cortex and other structures in the temporal lobe, and potentially the brain stem. A hematogenous route, which involves viral crossing of blood-brain barrier, is also possible. Secondary mechanisms involve hypoxia due to respiratory failure, as well as aberrant immune response leading to various forms of encephalopathy, white matter damage, and abnormal blood clotting resulting in stroke. Multiple neurological symptoms of COVID-19 have been described. These involve anosmia/ageusia, headaches, seizures, mental confusion and delirium, and coma. There is a growing concern that in a number of patients, long-term or perhaps even permanent cognitive impairment will persist well after the recovery from acute illness. Furthermore, COVID-19 survivors may be at increased risk for developing neurodegenerative diseases years or decades later. Since COVID-19 is a new disease, it will take months or even years to characterize the exact nature, scope, and temporal extent of its long-term neurocognitive sequelae. To that end, rigorous and systematic longitudinal follow-up will be required. For this effort to succeed, appropriate protocols and patient registries should be developed and put in place without delay now.