The coronavirus disease-19 (COVID-19) pandemic is an unprecedented worldwide health crisis. COVID-19 is caused by SARS-CoV-2, a highly infectious pathogen that is genetically similar to SARS-CoV. Similar to other recent coronavirus outbreaks, including SARS and MERS, SARS-CoV-2 infected patients typically present with fever, dry cough, fatigue, and lower respiratory system dysfunction, including high rates of pneumonia and acute respiratory distress syndrome (ARDS); however, a rapidly accumulating set of clinical studies revealed atypical symptoms of COVID-19 that involve neurological signs, including headaches, anosmia, nausea, dysgeusia, damage to respiratory centers, and cerebral infarction. These unexpected findings may provide important clues regarding the pathological sequela of SARS-CoV-2 infection. Moreover, no efficacious therapies or vaccines are currently available, complicating the clinical management of COVID-19 patients and emphasizing the public health need for controlled, hypothesis-driven experimental studies to provide a framework for therapeutic development. In this mini-review, we summarize the current body of literature regarding the central nervous system (CNS) effects of SARS-CoV-2 and discuss several potential targets for therapeutic development to reduce neurological consequences in COVID-19 patients.