Caching content at the edge network is a popular and effective technique widely deployed to alleviate the burden of network backhaul, shorten service delay and improve service quality. However, there has been some controversy over privacy violations in caching content at the edge network. On the one hand, the multi-access open edge network provides an ideal entrance or interface for external attackers to obtain private data from edge caches by extracting sensitive information. On the other hand, privacy can be infringed on by curious edge caching providers through caching trace analysis targeting the achievement of better caching performance or higher profits. Therefore, an in-depth understanding of privacy issues in edge caching networks is vital and indispensable for creating a privacy-preserving caching service at the edge network. In this article, we are among the first to fill this gap by examining privacy-preserving techniques for caching content at the edge network. Firstly, we provide an introduction to the background of privacy-preserving edge caching (PPEC). Next, we summarize the key privacy issues and present a taxonomy for caching at the edge network from the perspective of private information. Additionally, we conduct a retrospective review of the state-of-the-art countermeasures against privacy leakage from content caching at the edge network. Finally, we conclude the survey and envision challenges for future research.