Graphene-based vertical Schottky-barrier transistors (SBTs), renowned as graphene barristors, have emerged as a feasible candidate to fundamentally expand the horizon of conventional transistor technology. The remote tunability of graphene's electronic properties could endorse multi-stimuli responsive functionalities for a broad range of electronic and optoelectronic applications of transistors, with the capability of incorporating nanochannel architecture with dramatically reduced footprints from the vertical integrations. In this Feature Article, we provide a comprehensive overview of the progress made in the field of SBTs over the last 10 years, starting from the operating principles, materials evolution, and processing developments. Depending on the types of stimuli such as electrical, optical, and mechanical stresses, various fields of applications from conventional digital logic circuits to sensory technologies are highlighted. Finally, more advanced applications toward beyond-Moore electronics are discussed, featuring recent advancements in neuromorphic devices based on SBTs.