This article presents a comprehensive survey of the literature on self-interference (SI) in long-term evolution advanced (LTE-A) and fifth-generation (5G) new radio transceivers and should serve the reader as a guide and starting point for further work on SI management. Current trends in cellular transceiver designs are discussed, and reasons why new technologies, such as carrier aggregation, cause potential sensitivity degradation due to self-interfering signals are highlighted. The survey provides an overview of the most common interference mechanisms and continues with a taxonomy on SI mitigation architectures by comparing the strengths and weaknesses of various techniques.