In the past year, fifth-generation (5G) wireless technology has seen dramatic growth, spurred on by the continuing demand for faster data communications with lower latency. At the same time, many researchers argue that 5G will be inadequate in a short time, given the explosive growth of machine connectivity, such as the Internet-of-Things (IoT). This has prompted many to question what comes after 5G. The obvious answer is sixth-generation (6G), however, the substance of 6G is still very much undefined, leaving much to the imagination in terms of real-world implementation. What is clear, however, is that the next generation will likely involve the use of terahertz frequency (0.1&ndash / 10 THz) electromagnetic waves. Here, we review recent research in terahertz wireless communications and technology, focusing on three broad topic classes: the terahertz channel, terahertz devices, and space-based terahertz system considerations. In all of these, we describe the nature of the research, the specific challenges involved, and current research findings. We conclude by providing a brief perspective on the path forward.