During software development, developers make extensive use of third-party libraries to relieve themselves of heavy burden instead of reinventing common functions. There are dependencies between different third-party libraries. Incompatibilities between versions will lead to errors during installing, loading or invoking third-party libraries, resulting in system exceptions. Such problem is called Dependency Conflict (DC also referred as Conflict Dependency or CD) issue. The root cause of this issue is the third-party libraries fail to cover required features (e.g., methods). DC issues often occur at the project’s build time or runtime, and are difficult to locate. Repairing DC issues requires developers to know about the differencies among versions of third-party libraries they use, and the complex relationship between the third-party libraries increases the difficulty of repairment. In order to find DC issues before software running, and to respond to and deal with system anomalies caused by DC issues in the process of running, researchers have made various studies on these issues. This paper conducts a systematic review of this research topic from four aspects, including the usage analysis of third-party libraries, the root cause of DC issues, the detection methods of DC issues, and common fixing strategies. Finally, the potential research opportunities in the future are discussed, and references are provided for researchers in this field.