Novel coronavirus disease 2019 (COVID-19) has significantly altered the socio-economic status of countries. Although vaccines are now available against the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), a causative agent for COVID-19, it continues to transmit and newer variants of concern have been consistently emerging world-wide. Computational strategies involving drug repurposing offer a viable opportunity to choose a medication from a rundown of affirmed drugs against distinct diseases including COVID-19. While pandemics impede the healthcare systems, drug repurposing or repositioning represents a hopeful approach in which existing drugs can be remodeled and employed to treat newer diseases. In this review, we summarize the diverse computational approaches attempted for developing drugs through drug repurposing or repositioning against COVID-19 and discuss their advantages and limitations. To this end, we have outlined studies that utilized computational techniques such as molecular docking, molecular dynamic simulation, disease-disease association, drug-drug interaction, integrated biological network, artificial intelligence, machine learning and network medicine to accelerate creation of smart and safe drugs against COVID-19.