Graphene- and carbon-based nanomaterials are key materials to develop advanced biosensors for the sensitive detection of many biomarkers owing to their unique properties. Biosensors have attracted increasing interest because they allow efficacious, sensitive, selective, rapid, and low-cost diagnosis. Biosensors are analytical devices based on receptors for the process of detection and transducers for response measuring. Biosensors can be based on electrochemical, piezoelectric, thermal, and optical transduction mechanisms. Early virus identification provides critical information about potentially effective and selective therapies, extends the therapeutic window, and thereby reduces morbidity. The sensitivity and selectivity of graphene can be amended via functionalizing it or conjoining it with further materials. Amendment of the optical and electrical features of the hybrid structure by introducing appropriate functional groups or counterparts is especially appealing for quick and easy-to-use virus detection. Various techniques for the electrochemical detection of viruses depending on antigen–antibody interactions or DNA hybridization are discussed in this work, and the reasons behind using graphene and related carbon nanomaterials for the fabrication are presented and discussed. We review the existing state-of-the-art directions of graphene-based classifications for detecting DNA, protein, and hormone biomarkers and summarize the use of the different biosensors to detect several diseases, like cancer, Alzheimer’s disease, and diabetes, to sense numerous viruses, including SARS-CoV-2, human immunodeficiency virus, rotavirus, Zika virus, and hepatitis B virus, and to detect the recent pandemic virus COVID-19. The general concepts, mechanisms of action, benefits, and disadvantages of advanced virus biosensors are discussed to afford beneficial evidence of the creation and manufacture of innovative virus biosensors. We emphasize that graphene-based nanomaterials are ideal candidates for electrochemical biosensor engineering due to their special and tunable physicochemical properties.