As big data and computing power rapidly develop, deep learning has made significant breakthroughs and rapidly become a field with numerous practical application scenarios and active research topics. In response to the growing demand for the development of deep learning tasks, deep learning frameworks have arisen. Acting as an intermediate component between application scenarios and hardware platforms, deep learning frameworks facilitate the development of deep learning applications, enabling users to efficiently construct diverse deep neural network (DNN) models, and deeply adapt to various computing hardware, meeting the computational needs across different computing architectures and environments. Any issues that arise within deep learning frameworks, which serve as the fundamental software in the realm of artificial intelligence, can have severe consequences. Even a single bug in the code can trigger widespread failures within models built upon the framework, thereby posing a serious threat to the safety of deep learning systems. As the first review exclusively focuses on the testing of deep learning frameworks, this study initially introduces the developmental history and basic architectures of deep learning frameworks. Subsequently, by systematically examining 55 academic papers directly related to the testing of deep learning frameworks, the study systematically analyzes and summarizes bug characteristics, key technologies for testing, and methods based on various input forms for testing. The study explores how to combine key technologies to address research problems. Lastly, it summarizes the unresolved difficulties in the testing of deep learning frameworks and provides insights into promising research directions for the future. This study can offer valuable references and guidance to individuals involved in the research field of deep learning framework testing, ultimately promoting the sustained development and maturity of deep learning frameworks.