As the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) epidemic spreads, it is becoming increasingly evident that coronavirus disease 2019 (COVID-19) is not limited to the respiratory system, and that other organs can be affected. In particular, virus-related neurological manifestations are being reported more and more frequently in the scientific literature. In this article, we review the literature on the association between COVID-19 and neurological manifestations, present evidence from preclinical research suggesting that SARS-CoV-2 could be responsible for many of these manifestations, and summarize the biological pathways that could underlie each neurological symptom. Understanding the mechanisms that lead to neurological manifestations in patients with COVID-19 and how these manifestations correlate with clinical outcomes will be instrumental in guiding the optimal use of targeted therapeutic strategies.