With the rise of large language and vision-language models, AI agents have evolved into autonomous, interactive systems capable of perception, reasoning, and decision-making. As they proliferate across virtual and physical domains, the Internet of Agents (IoA) has emerged as a key infrastructure for enabling scalable and secure coordination among heterogeneous agents. This survey offers a comprehensive examination of the security and privacy landscape in IoA systems. We begin by outlining the IoA architecture and its distinct vulnerabilities compared to traditional networks, focusing on four critical aspects: identity authentication threats, cross-agent trust issues, embodied security, and privacy risks. We then review existing and emerging defense mechanisms and highlight persistent challenges. Finally, we identify open research directions to advance the development of resilient and privacy-preserving IoA ecosystems.