Field-effect transistor (FET) is a very promising platform for biosensor applications due to its magnificent properties, including label-free detection, high sensitivity, fast response, real-time measurement capability, low running power, and the feasibility to miniaturize to a portable device. 1D (e.g. carbon nanotubes, Si nanowires, conductive polymer nanowires, 1D metal oxides, and others) and 2D (e.g. graphene materials, transition metal dichalcogenides, black phosphorus, and 2D metal oxides) materials, with their unique structural and electronic properties that are unavailable in bulk materials, have helped improve the sensitivity of FET biosensors and enabled detection down to single molecule. In this article, we give insights into the rapidly evolving field of 1D and 2D materials-based FET biosensors, with an emphasis on structure and electronic properties, synthesis, and biofunctionalization approaches of these nanomaterials. In addition, the progress in the 1D/2D-FET biosensors in North America, in the last decade, is summarized in tables. Moreover, challenges and future perspectives of 1D/2D-FET biosensors are covered.