We assume that Zipf's law governs the accesses in the Web. Based on this assumption, we show that caching Web objects can lead to very high hit rates. Furthermore, we can calculate the size of the cache that is required to achieve a given hit ratio. Assuming that Zipf's law continually applies to accesses of Internet objects, we argue that a cache replacement policy based on the concept or the Least Frequently Used object suffices to obtain the theoretically achievable results, assuming a large enough cache. Using this theory, we show how results available in the literature can be explained. We also show how a designer can make decisions and develop caching architectures for networks based on the profiles of average users. We propose clip- based caching of video objects rather than caching of complete objects. Clips are disseminated in video library and browsing environments and are small enough to be properly managed by a cache scheme based on Zipf's law.