Resonant tunnelling diode (RTD) technology is emerging as one of the promising semiconductor-based solidstate technologies for terahertz (THz) wireless communications. This paper provides a review of the state-of-the-art, with a focus on the THz RTD oscillator, which is the key component of RTDbased THz transmitters and coherent receivers. A brief summary on the device principle of operation, technology, modelling, as well as an overview of oscillator design and implementation approaches for THz emitters, is provided. A new insight to device evaluation and to the reported oscillator performance levels is also given, together with brief remarks on RTD-based THz detectors. Thereafter, an overview of the reported wireless links which utilise an RTD in either transmission or reception, or in both roles, is given. Highlight results include the record single-channel wireless data rate of 56 Gb/s employing an all RTD-based transceiver, which demonstrates the potential of the technology for future short-range communications. The paper concludes with a discussion of the current technical challenges and possible strategies for future progress.