Mankind is currently living in the era of mobile communication. Mobile communication encompasses almost all areas of our daily life and is heavily used in most sectors of economy, including agriculture, healthcare, education, and so on. With mobile devices such as smart phones, people can connect to any other people somewhere on the earth, can access huge databases via the internet, stream videos and movies, to name just a few of the many mobile services that are routinely used in the early 2020s. Artificial intelligence, virtual reality, and other emerging new applications will further boost the importance of mobile communication. It is a general trend that with progressing evolution of mobile communication, the amount of data to be transmitted wirelessly increases rapidly and continuously. To enable this, a suitable well-performing hardware infrastructure is needed. The hardware used so far in the successively introduced generations of systems for mobile communication is essentially based on fast transistors. We designate these transistors as gigahertz (GHz)–terahertz (THz) transistors, as the high data rates to be transferred require an electronic hardware operating properly at frequencies in the GHz–THz range. The present paper provides a comprehensive in-depth discussion of these transistors. After a short survey of the evolution of mobile communication systems, the different categories and classes of GHz–THz transistors are introduced, relevant transistor performance measures called figures of merit are defined, issues of transistor design are dealt with, and general design rules for GHz–THz transistors are established. This is followed by a tour through the evolution of these transistors, starting in the 1950s, when the first transistors with GHz capabilities were demonstrated, up to the latest developments since the turn of the millennium and to the state-of-the-art in mid-2024. The discussion includes evolutionary advances as well as true breakthroughs, both contributing to the significant performance improvements achieved over the years. Furthermore, some research activities on GHz–THz transistors, which, unfortunately, led to a dead end as well as ongoing efforts with still unclear outcome are presented and the approaching limits of transistor performance are critically examined. Finally, we take a short view on alternative hardware options for mobile communication systems beyond the limits of transistors.