The widespread use of the Internet and the maturing of digital video technology have led to an increase in various streaming media applications. As broadband to the home becomes more prevalent, the bottleneck of delivering quality streaming media is shifting upstream to the backbone, peering links, and the best-effort Internet. In this paper, we address the problem of efficiently streaming video assets to the end clients over a distributed infrastructure consisting of origin servers and proxy caches. We build on earlier work and propose a unified mathematical framework under which various server scheduling and proxy cache management algorithms for video streaming can be analyzed. More precisely, we incorporate known server scheduling algorithms (batching/patching/batchpatching) and proxy caching algorithms (full/partial/no caching with or without caching patch bytes) in our framework and analyze the minimum backbone bandwidth consumption under the optimal joint scheduling and caching strategies. We start by studying the optimal policy for streaming a single video object and derive a simple heuristic to enable management of multiple heterogeneous videos efficiently. We then show that the performance of our heuristic is close to that of the optimal scheme, under a wide range of parameters.