In this review, the suitability of the major types of carbon nanostructures as conducting channels of field-effect transistors (FETs) is compared on the basis of the dimensionality and size of their pi-conjugated system. For each of these materials, recent progress in its synthesis, electrical and structural characterization, as well as its implementation into various gate configurations is surveyed, with emphasis laid onto nanoscale aspect of the FET design and the attainable device performance. Finally, promising future research directions, such as the integration of different carbon nanostructures into novel device architectures, are outlined.