Owing to its outstanding physical properties, graphene has attracted attention as a promising biosensor material. Field-effect-transistor (FET)-based biosensors are particularly promising because of their high sensitivity that is achieved through the high carrier mobility of graphene. However, graphene-FET biosensors have not yet reached widespread practical applications owing to several problems. In this review, the authors focus on graphene-FET biosensors and discuss their advantages, the challenges to their development, and the solutions to the challenges. The problem of Debye screening, in which the surface charges of the detection target are shielded and undetectable, can be solved by using small-molecule receptors and their deformations and by using enzyme reaction products. To address the complexity of sample components and the detection mechanisms of graphene-FET biosensors, the authors outline measures against nonspecific adsorption and the remaining problems related to the detection mechanism itself. The authors also introduce a solution with which the molecular species that can reach the sensor surfaces are limited. Finally, the authors present multifaceted approaches to the sensor surfaces that provide much information to corroborate the results of electrical measurements. The measures and solutions introduced bring us closer to the practical realization of stable biosensors utilizing the superior characteristics of graphene.