Biosensors are measurement devices that can sense several biomolecules, and are widely used for the detection of relevant clinical pathogens such as bacteria and viruses, showing outstanding results. Because of the latent existing risk of facing another pandemic like the one we are living through due to COVID-19, researchers are constantly looking forward to developing new technologies for diagnosis and treatment of infections caused by different bacteria and viruses. Regarding that, nanotechnology has improved biosensors’ design and performance through the development of materials and nanoparticles that enhance their affinity, selectivity, and efficacy in detecting these pathogens, such as employing nanoparticles, graphene quantum dots, and electrospun nanofibers. Therefore, this work aims to present a comprehensive review that exposes how biosensors work in terms of bacterial and viral detection, and the nanotechnological features that are contributing to achieving a faster yet still efficient COVID-19 diagnosis at the point-of-care.