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Streaming media has contributed to a significant amount of today's Internet traffic. Like conventional Web objects (e.g., HTML pages and images), media objects can benefit from proxy caching; but their unique features such as huge size and high bandwidth demand imply that conventional proxy caching strategies have to be substantially revised. This article discusses the critical issues and challenges of cache management for proxy-assisted media streaming. We survey, classify, and compare the state-of-the-art solutions. We also investigate advanced issues of combining multicast with caching, cooperating among proxies, and leveraging proxy caching in overlay networks.