During software development, developers use third-party libraries extensively to achieve code reuse. Due to the dependencies among different third-party libraries, the incompatibilities among them lead to errors during the installing, loading, or calling of those libraries and ultimately result in system anomalies. Such a problem is called a dependency conflict (DC, also referred to as conflict dependency or CD) issue of third-party libraries. The root cause of such issues is that the third-party libraries loaded fail to cover the required features (e.g., methods) cited by the software. DC issues often occur during the download and install, project compiling, and running of third-party libraries and are difficult to locate. Fixing DC issues requires developers to know the differences among the versions of the third-party libraries they use accurately, and the complex dependencies among the third-party libraries increase the difficulty in this work. To identify the DC issues in the software before its running and to deal with the system anomalies caused by those issues during running, researchers around the world have conducted various studies on such issues. This study presents a systematic review of this research topic from four aspects, including the empirical analysis of third-party library usage, the cause analysis of DC issues, and the detection methods and common fixing ways for such issues. Finally, the potential research opportunities in this field are discussed.