Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) caused an outbreak in Wuhan city, China and quickly spread worldwide. Currently, there are no specific drugs or antibodies that claim to cure severe acute respiratory diseases. For SARS-CoV-2, the spike (S) protein recognizes and binds to the angiotensin converting enzyme 2 (ACE2) receptor, allowing viral RNA to enter the host cell. The main protease (Mpro) is involved in the proteolytic process for mature non-structural proteins, and RNA-dependent RNA polymerase (RdRp) is responsible for the viral genome replication and transcription processes. Owing to the pivotal physiological roles in viral invasion and replication, S protein, Mpro, RdRp are regarded as the main therapeutic targets for coronavirus disease 2019 (COVID-19). In this review, we carried out an evolutionary analysis of SARS-CoV-2 in comparison with other mammal-infecting coronaviruses that have sprung up in the past few decades and described the pathogenic mechanism of SARS-CoV-2. We displayed the structural details of S protein, Mpro, and RdRp, as well as their complex structures with different chemical inhibitors or antibodies. Structural comparisons showed that some neutralizing antibodies and small molecule inhibitors could inhibit S protein, Mpro, or RdRp. Moreover, we analyzed the structural differences between SARS-CoV-2 ancestral S protein and D614G mutant, which led to a second wave of infection during the recent pandemic. In this context, we outline the methods that might potentially help cure COVID-19 and provide a summary of effective chemical molecules and neutralizing antibodies.