The coronavirus disease 2019 (COVID-19) is currently a new public health crisis threatening the world. This pandemic disease is caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The virus has been reported to be originated in bats, and by yet unknown intermediary animals were transmitted to humans in China 2019. The SARS-CoV-2 spreads faster than its two ancestors, the SARS-CoV and Middle East respiratory syndrome coronavirus (MERS-CoV) but has reduced fatality. At present, the SARS-CoV-2 has caused about 1.16 million deaths with more than 43.4 million confirmed cases worldwide, resulting in a serious threat to public health globally with yet uncertain impact. The disease is transmitted by inhalation or direct contact with an infected person. The incubation period ranges from 1 to 14 days. COVID-19 is accompanied by various symptoms, including cough and fatigue. In most people, the disease is mild, but in some other people, such as in the elderly and people with chronic diseases, it may progress from pneumonia to a multi-organ dysfunction. Many people are reported asymptomatic. The virus genome is sequenced, but new variants are reported. Numerous biochemical aspects of its structure and function are revealed. To date, no clinically approved vaccines and/or specific therapeutic drugs are available to prevent or treat COVID-19. However, there are reported intensive researches on the SARS-CoV-2 to potentially identify vaccines and/or drug targets, which may help to overcome the disease. In this review, we discuss recent advances in understanding the molecular structure of SARS-CoV-2 and its biochemical characteristics.