The outbreak of coronavirus disease 2019 (COVID-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), has attracted increasing worldwide attention. Cases of liver damage or dysfunction (mainly characterized by moderately elevated serum aspartate aminotransferase levels) have been reported among patients with COVID-19. However, it is currently uncertain whether the COVID-19-related liver damage/dysfunction is due mainly to the viral infection per se or other coexisting conditions, such as the use of potentially hepatotoxic drugs and the coexistence of systemic inflammatory response, respiratory distress syndrome-induced hypoxia, and multiple organ dysfunction. Based on the current evidence from case reports and case series, this review article focuses on the demographic and clinical characteristics, potential mechanisms, and treatment options for COVID-19-related liver dysfunction. This review also describes the geographical and demographic distribution of COVID-19-related liver dysfunction, as well as possible underlying mechanisms linking COVID-19 to liver dysfunction, in order to facilitate future drug development, prevention, and control measures for COVID-19.