Our recent experience of the COVID-19 pandemic has highlighted the importance of easy-to-use, quick, cheap, sensitive and selective detection of virus pathogens for the efficient monitoring and treatment of virus diseases. Early detection of viruses provides essential information about possible efficient and targeted treatments, prolongs the therapeutic window and hence reduces morbidity. Graphene is a lightweight, chemically stable and conductive material that can be successfully utilized for the detection of various virus strains. The sensitivity and selectivity of graphene can be enhanced by its functionalization or combination with other materials. Introducing suitable functional groups and/or counterparts in the hybrid structure enables tuning of the optical and electrical properties, which is particularly attractive for rapid and easy-to-use virus detection. In this review, we cover all the different types of graphene-based sensors available for virus detection, including, e.g., photoluminescence and colorimetric sensors, and surface plasmon resonance biosensors. Various strategies of electrochemical detection of viruses based on, e.g., DNA hybridization or antigen-antibody interactions, are also discussed. We summarize the current state-of-the-art applications of graphene-based systems for sensing a variety of viruses, e.g., SARS-CoV-2, influenza, dengue fever, hepatitis C virus, HIV, rotavirus and Zika virus. General principles, mechanisms of action, advantages and drawbacks are presented to provide useful information for the further development and construction of advanced virus biosensors. We highlight that the unique and tunable physicochemical properties of graphene-based nanomaterials make them ideal candidates for engineering and miniaturization of biosensors.