For more than 50 years, silicon transistors have been continuously shrunk to meet the projections of Moore's law but are now reaching fundamental limits on speed and power use. With these limits at hand, nanomaterials offer great promise for improving transistor performance and adding new applications through the coming decades. With different transistors needed in everything from high-performance servers to thin-film display backplanes, it is important to understand the targeted application needs when considering new material options. Here the distinction between high-performance and thin-film transistors is reviewed, along with the benefits and challenges to using nanomaterials in such transistors. In particular, progress on carbon nanotubes, as well as graphene and related materials (including transition metal dichalcogenides and X-enes), outlines the advances and further research needed to enable their use in transistors for high-performance computing, thin films, or completely new technologies such as flexible and transparent devices.