The COVID-19 pandemic has severely impacted normal human life worldwide. Due to its rapid community spread and high mortality statistics, the development of prompt diagnostic tests for a massive number of samples is essential. Currently used traditional methods are often expensive, time-consuming, laboratory-based, and unable to handle a large number of specimens in resource-limited settings. Because of its high contagiousness, efficient identification of SARS-CoV-2 carriers is crucial. As the advantages of adopting biosensors for efficient diagnosis of COVID-19 increase, this narrative review summarizes the recent advances and the respective reasons to consider applying biosensors. Biosensors are the most sensitive, specific, rapid, user-friendly tools having the potential to deliver point-of-care diagnostics beyond traditional standards. This review provides a brief introduction to conventional methods used for COVID-19 diagnosis and summarizes their advantages and disadvantages. It also discusses the pathogenesis of COVID-19, potential diagnostic biomarkers, and rapid diagnosis using biosensor technology. The current advancements in biosensing technologies, from academic research to commercial achievements, have been emphasized in recent publications. We covered a wide range of topics, including biomarker detection, viral genomes, viral proteins, immune responses to infection, and other potential proinflammatory biomolecules. Major challenges and prospects for future application in point-of-care settings are also highlighted.