As a lightweight and robust brain-inspired computing paradigm, Hyperdimensional Computing (HDC) serves as a promising solution for the next-generation edge AI. However, the basic form of HDC is vulnerable to privacy leaks and cyber attacks. In this paper, we breifly review and discuss the recent contributions to privacy and security of HDC. We first summarize existing HDC designs to protect against privacy leaks, such as differential privacy. Next, we review the data encryption techniques for collaborative learning using HDC based on Multi-Party Computation and Homomorphic Encryption. Finally, we discuss the HDC-based designs for combating cyber attacks in a malicious environment. More research on private and secure HDC-based methods are needed for future large-scale edge deployment.