In this paper we will investigate transformations that serve as tools in the design of new data structures. Specifically, we study general methods for converting static structures (in which all elements are known before any searches are performed) to dynamic structures (in which the insertion of a new element can be mixed with searches). We will see three classes of such transformations (each based on a different counting scheme for representing the integers) and then use a combinatorial model to show the optimality of many of the transformations. Issues such as online data structures and deletion of elements are also examined. To demonstrate the applicability of these tools, we will study six new data structures that have been developed by applying the transformations.