SARS-CoV-2 has infected hundreds of millions of people with over four million dead, resulting in one of the worst global pandemics in recent history. Neurological symptoms associated with COVID-19 include anosmia, ageusia, headaches, confusion, delirium, and strokes. These may manifest due to viral entry into the central nervous system (CNS) through the blood-brain barrier (BBB) by means of ill-defined mechanisms. Here, we summarize the abilities of SARS-CoV-2 and other neurotropic RNA viruses, including Zika virus and Nipah virus, to cross the BBB into the CNS, highlighting the role of magnetic resonance imaging (MRI) in assessing presence and severity of brain structural changes in COVID-19 patients. We present new insight into key mutations in SARS-CoV-2 variants B.1.1.7 (P681H) and B.1.617.2 (P681R), which may impact on neuropilin 1 (NRP1) binding and CNS invasion. We postulate that SARS-CoV-2 may infect both peripheral cells capable of crossing the BBB and brain endothelial cells to traverse the BBB and spread into the brain. COVID-19 patients can be followed up with MRI modalities to better understand the long-term effects of COVID-19 on the brain.