Viral infections are among the main reasons for serious pandemics and contagious infections; hence, they cause thousands of fatalities and economic losses annually. In the case of COVID-19, world economies have shut down for months, and physical distancing along with drastic changes in the social behavior of many humans has generated many issues for all countries. Thus, a rapid, low-cost, and sensitive viral detection method is critical to upgrade the living standards of humans while exploiting biomedicine, environmental science, bioresearch, and biosecurity. The emergence of various carbon-based nanomaterials such as carbon nanotubes, graphene, and carbon nanoparticles provided a great possibility for researchers to develop a new and wide variety of biosensors. In particular, graphene has become a promising tool for biosensor fabrication owing to its many interesting properties, such as its exceptional conductivity, ultrahigh electron mobility, and excellent thermal conductivity. This paper provides an overall perspective of graphene-based biosensors and a critical review of the recent advances in graphene-based biosensors that are used to detect different types of viruses, such as Ebola, Zika, and influenza.