Full-duplex (FD) communication is a potential game changer for future wireless networks. It allows for simultaneous transmit and receive operations over the same frequency band, a doubling of the spectral efficiency. FD can also be a catalyst for supercharging other existing/emerging wireless technologies, including cooperative and cognitive communications, cellular networks, multiple-input multiple-output (MIMO), massive MIMO, non-orthogonal multiple access (NOMA), millimeterwave (mmWave) communications, unmanned aerial vehicle (UAV)-aided communication, backscatter communication (Back-Com), and reconfigurable intelligent surfaces (RISs). These integrated technologies can further improve spectral efficiency, enhance security, reduce latency, and boost the energy efficiency of future wireless networks. A comprehensive survey of such integration has thus far been lacking. This paper fills that need. Specifically, we first discuss the fundamentals, highlighting the FD transceiver structure and the self-interference (SI) cancellation techniques. Next, we discuss the coexistence of FD with the above-mentioned wireless technologies. We also provide case studies for some of the integration scenarios mentioned above and future research directions for each case. We further address the potential research directions, open challenges, and applications for future FD-assisted wireless, including cell-free massive MIMO, mmWave communications, UAV, BackCom, and RISs. Finally, potential applications and developments of other miscellaneous technologies, such as mixed radio-frequency/freespace optical, visible light communication, dual-functional radarcommunication, underwater wireless communication, multi-user ultra-reliable low-latency communications, vehicle-to-everything communications, rate splitting multiple access, integrated sensing and communication, and age of information, are also highlighted.