As a definition, Human–Machine Interface (HMI) enables a person to interact with a device. Starting from elementary equipment, the recent development of novel techniques and unobtrusive devices for biosignals monitoring paved the way for a new class of HMIs, which take such biosignals as inputs to control various applications. The current survey aims to review the large literature of the last two decades regarding biosignal-based HMIs for assistance and rehabilitation to outline state-of-the-art and identify emerging technologies and potential future research trends. PubMed and other databases were surveyed by using specific keywords. The found studies were further screened in three levels (title, abstract, full-text), and eventually, 144 journal papers and 37 conference papers were included. Four macrocategories were considered to classify the different biosignals used for HMI control: biopotential, muscle mechanical motion, body motion, and their combinations (hybrid systems). The HMIs were also classified according to their target application by considering six categories: prosthetic control, robotic control, virtual reality control, gesture recognition, communication, and smart environment control. An ever-growing number of publications has been observed over the last years. Most of the studies (about 67%) pertain to the assistive field, while 20% relate to rehabilitation and 13% to assistance and rehabilitation. A moderate increase can be observed in studies focusing on robotic control, prosthetic control, and gesture recognition in the last decade. In contrast, studies on the other targets experienced only a small increase. Biopotentials are no longer the leading control signals, and the use of muscle mechanical motion signals has experienced a considerable rise, especially in prosthetic control. Hybrid technologies are promising, as they could lead to higher performances. However, they also increase HMIs’ complexity, so their usefulness should be carefully evaluated for the specific application.