The importance of coronaviruses as human pathogen has been highlighted by the recent outbreak of SARS-CoV-2 leading to the search of suitable drugs to overcome respiratory infections caused by the virus. Due to the lack of specific drugs against coronavirus, the existing antiviral and antimalarial drugs are currently being administered to the patients infected with SARS-CoV-2. The scientists are also considering repurposing of some of the existing drugs as a suitable option in search of effective drugs against coronavirus till the establishment of a potent drug and/or vaccine. Computer-aided drug discovery provides a promising attempt to enable scientists to develop new and target specific drugs to combat any disease. The discovery of novel targets for COVID-19 using computer-aided drug discovery tools requires knowledge of the structure of coronavirus and various target proteins present in the virus. Targeting viral proteins will make the drug specific against the virus, thereby, increasing the chances of viral mortality. Hence, this review provides the structure of SARS-CoV-2 virus along with the important viral components involved in causing infection. It also focuses on the role of various target proteins in disease, the mechanism by which currently administered drugs act against the virus and the repurposing of few drugs. The gap arising from the absence of specific drugs is addressed by proposing potential antiviral drug targets which might provide insights into structure-based drug development against SARS-CoV-2.