Coronavirus disease 2019 (COVID-19), caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), has led to a global pandemic. Although COVID-19 was initially described as a respiratory disease, there is growing evidence that SARS-CoV-2 is able to invade the brains of COVID-19 patients and cause cognitive impairment. It has been reported that SARS-CoV-2 may have invasive effects on a variety of cranial nerves, including the olfactory, trigeminal, optic, and vagus nerves, and may spread to other brain regions via infected nerve endings, retrograde transport, and transsynaptic transmission. In addition, the blood-brain barrier (BBB), composed of neurovascular units (NVUs) lining the brain microvasculature, acts as a physical barrier between nerve cells and circulating cells of the immune system and is able to regulate the transfer of substances between the blood and brain parenchyma. Therefore, the BBB may be an important structure for the direct and indirect interaction of SARS-CoV-2 with the brain via the blood circulation. In this review, we assessed the potential involvement of neuroinvasion under the SARS-CoV-2 infection, and the potential impact of BBB disorder under SARS-CoV-2 infection on cognitive impairment.