Deep learning frameworks promote the development of artificial intelligence and demonstrate considerable potential in numerous applications. However, the security issues of deep learning frameworks are among the main risks preventing the wide application of it. Attacks on deep learning frameworks by malicious internal or external attackers would exert substantial effects on society and life. We start with a description of the framework of deep learning algorithms and a detailed analysis of attacks and vulnerabilities in them. We propose a highly comprehensive classification approach for security issues and defensive approaches in deep learning frameworks and connect different attacks to corresponding defensive approaches. Moreover, we analyze a case of the physical-world use of deep learning security issues. In addition, we discuss future directions and open issues in deep learning frameworks. We hope that our research will inspire future developments and draw attention from academic and industrial domains to the security of deep learning frameworks.