Many systems have been designed for the detection of SARS-CoV-2, which is the virus that causes COVID-19. SARS-CoV-2 is readily transmitted, resulting in the rapid spread of disease in human populations. Frequent testing at the point of care (POC) is a key aspect for controlling outbreaks caused by SARS-CoV-2 and other emerging pathogens, as the early identification of infected individuals can then be followed by appropriate measures of isolation or treatment, maximizing the chances of recovery and preventing infectious spread. Diagnostic tools used for high-frequency testing should be inexpensive, provide a rapid diagnostic response without sophisticated equipment, and be amenable to manufacturing on a large scale. The application of these devices should enable large-scale data collection, help control viral transmission, and prevent disease propagation. Here we review functional nanomaterial-based optical and electrochemical biosensors for accessible POC testing for COVID-19. These biosensors incorporate nanomaterials coupled with paper-based analytical devices and other inexpensive substrates, traditional lateral flow technology (antigen and antibody immunoassays), and innovative biosensing methods. We critically discuss the advantages and disadvantages of nanobiosensor-based approaches compared to widely used technologies such as PCR, ELISA, and LAMP. Moreover, we delineate the main technological, (bio)chemical, translational, and regulatory challenges associated with developing functional and reliable biosensors, which have prevented their translation into the clinic. Finally, we highlight how nanobiosensors, given their unique advantages over existing diagnostic tests, may help in future pandemics.