Preserving privacy in communication and networking is of paramount importance in the Internet-of-Everything age of escalating surveillance and data collection. Anonymous communication is a cornerstone of this endeavor, enabling individuals to interact and exchange private information without disclosing their identities. However, achieving absolute security and privacy in classical anonymous networks (CANs) is highly challenging, and in particular, the advent of quantum computing poses critical threats to securing classical communication. In this article, we explore the evolution of CANs and delve into the distinctive shift from classical to quantum anonymous networks (QANs), emphasizing a substantial leap in privacy protected by quantum anonymous communication (QAC). The fundamental motivations behind this transition are rooted in the remarkable privacy attributes—e.g., complete anonymity and untraceability —of QAC protocols, as well as the unconditional security ensured by the principles of quantum mechanics. To make these concepts more tangible in practical settings and provide a benchmark to design the QAC protocols in QANs, we usher in exemplary protocols: quantum anonymous teleportation, voting, and information retrieval. In these case studies, we assess the fidelity and error rates of the QAC protocols in noisy environments, aiming to evaluate their robustness in practical quantum entangled settings. Moreover, we discuss the primary challenges and future research directions integral to the transition towards QANs.