Increased demand for higher spectrum efficiency, especially in the space-limited chip, base station, and vehicle environments, has spawned the development of full-duplex communications, which enable the transmitting and receiving to occur simultaneously at the same frequency. The key challenge in this full-duplex communication paradigm is to reduce the self-interference as much as possible, ideally, down to the noise floor. This paper provides a comprehensive review of the self-interference cancellation (SIC) techniques for co-located communication systems from a circuits and fields perspective. The self-interference occurs when the transmitting antenna and the receiving antenna are co-located, which significantly degrade the system performance of the receiver, in terms of the receiver desensitization, signal masking, or even damage of hardwares. By introducing the SIC techniques, the self-interference can be suppressed and the weak desired signal from the remote transmitter can be recovered. This, therefore, enables the full-duplex communications to come into the picture. The SIC techniques are classified into two main categories: the traditional circuit-domain SICs and the novel field-domain SICs, according to the method of how to rebuild and subtract the self-interference signal. In this review paper, the field-domain SIC method is systematically summarized for the first time, including the theoretical analysis and the application remarks. Some typical SIC approaches are presented and the future works are outlooked.