Electronic devices based on carbon nanotubes are among the candidates to eventually replace silicon-based devices for logic applications. Before then, however, nanotube-based radiofrequency transistors could become competitive for high-performance analogue components such as low-noise amplifiers and power amplifiers in wireless systems. Single-walled nanotubes are well suited for use in radiofrequency transistors because they demonstrate near-ballistic electron transport and are expected to have high cut-off frequencies. To achieve the best possible performance it is necessary to use dense arrays of semiconducting nanotubes with good alignment between the nanotubes, but techniques that can economically manufacture such arrays are needed to realize this potential. Here we review progress towards nanotube electronics for radiofrequency applications in terms of device physics, circuit design and the manufacturing challenges.