We study the bounds and means of optimal caching in overlay Content Distribution Networks (CDN) that serve data with dynamic content to end-users who send random requests for the most up-to-date version of such content. Applications with such dynamic content are numerous, including daily news, weather conditions, stock market prices, social networking messages, etc. The service for such a dynamically changing content necessitates a fundamentally different approach than traditional pull-based (also called non-proactive) schemes. In particular, proactive caching is required to optimize the type and amount of content to be updated in the local servers of a CDN hence minimize the transmission and caching costs, subject to storage constraints. We study the metric of cost reduction achieved by proactive caching over non-proactive caching strategies. We introduce the notion of popularity to establish fundamental upper and lower bounds on cost reduction under different degrees of storage space constraints. We prove the lower bounds to achieve the optimal rate of increase achieved by the upper bounds as the database of items increases. In particular, for a general form of convex, superlinear and monotonically increasing cost functions, our results reveal that the optimal cost reduction scales as the cost function itself, or at least as its first derivative, depending on the number of popular data items, as well as the cache storage capacity.