In recent years, emerging non-volatile memory (NVM) technologies, such as phase change memory (PCM), spin-transfer torque RAM (STT-RAM), and memristor have gained great attention of researchers. NVM has both byte-addressable and non-volatile features, thereby making it possible to replace both traditional main memory and persistent storage. Also, NVM can be used in hybrid memory and storage architecture. Due to the advantages of low latency, high density, and low power, NVM has become the promising memory technology because of the effect of alleviating memory wall problem. However, applications can access NVM directly through ordinary load/store interface, and more important, data resided in the NVM still retains after power loss, thus it imposes new challenges of security and privacy. This paper surveys several security problems about NVM and existing solutions including persistent memory leak, stray writes, metadata security, malicious wearout attacks, and non-volatile pointer. Then, privacy issues and existing studies about NVM, such as data protection and information leaks, are discussed. Finally, we explore other potential security and privacy issues related to NVM and propose several possible solutions, such as convergence of permission and protection, security of non-volatile cache, volatile NVM, and program security.