In-band full-duplex (IBFD) wireless has emerged as a promising solution to increase the throughput of wireless communication systems. IBFD allows a wireless terminal to transmit and receive simultaneously in the same frequency band, potentially doubling spectral efficiency. However, self-interference, caused by the terminal's own transmissions interfering with its desired receptions, remains a major challenge. This paper reviews the main concepts of IBFD wireless, discusses various self-interference mitigation techniques, and explores research challenges and opportunities in the design and analysis of IBFD systems. IBFD has been used in radar systems since the 1940s, with early techniques relying on antenna separation and circulators for isolation. In recent years, IBFD has gained attention in wireless communication systems, particularly for improving spectral efficiency. However, practical implementation faces challenges due to the high levels of self-interference, which can be mitigated through propagation-domain, analog-circuit-domain, and digital-domain techniques. Propagation-domain techniques aim to isolate the transmit and receive chains through path loss, cross-polarization, and antenna directionality. Analog-circuit-domain techniques involve tapping the transmit signal and subtracting it from the receive signal in the analog domain. Digital-domain techniques use sophisticated signal processing to cancel self-interference after the ADC. Each approach has its advantages and limitations, with digital-domain techniques being limited by the ADC's dynamic range. IBFD has the potential to significantly improve the spectral efficiency of future wireless networks, but challenges remain in achieving practical implementation. Research is ongoing to develop more effective self-interference cancellation techniques, improve the design of IBFD terminals, and explore new applications in wireless communication systems. The paper also discusses the importance of channel-state information in managing self-interference and the potential of IBFD in various network topologies, including relays, bidirectional communication, and base stations. Overall, IBFD offers promising opportunities for enhancing wireless communication systems, but further research is needed to overcome the challenges associated with self-interference and practical implementation.In-band full-duplex (IBFD) wireless has emerged as a promising solution to increase the throughput of wireless communication systems. IBFD allows a wireless terminal to transmit and receive simultaneously in the same frequency band, potentially doubling spectral efficiency. However, self-interference, caused by the terminal's own transmissions interfering with its desired receptions, remains a major challenge. This paper reviews the main concepts of IBFD wireless, discusses various self-interference mitigation techniques, and explores research challenges and opportunities in the design and analysis of IBFD systems. IBFD has been used in radar systems since the 1940s, with early techniques relying on antenna separation and circulators for isolation. In recent years, IBFD has gained attention in wireless communication systems, particularly for improving spectral efficiency. However, practical implementation faces challenges due to the high levels of self-interference, which can be mitigated through propagation-domain, analog-circuit-domain, and digital-domain techniques. Propagation-domain techniques aim to isolate the transmit and receive chains through path loss, cross-polarization, and antenna directionality. Analog-circuit-domain techniques involve tapping the transmit signal and subtracting it from the receive signal in the analog domain. Digital-domain techniques use sophisticated signal processing to cancel self-interference after the ADC. Each approach has its advantages and limitations, with digital-domain techniques being limited by the ADC's dynamic range. IBFD has the potential to significantly improve the spectral efficiency of future wireless networks, but challenges remain in achieving practical implementation. Research is ongoing to develop more effective self-interference cancellation techniques, improve the design of IBFD terminals, and explore new applications in wireless communication systems. The paper also discusses the importance of channel-state information in managing self-interference and the potential of IBFD in various network topologies, including relays, bidirectional communication, and base stations. Overall, IBFD offers promising opportunities for enhancing wireless communication systems, but further research is needed to overcome the challenges associated with self-interference and practical implementation.