The Overture Framework is an object-oriented environment for solving PDEs on serial and parallel architectures. It is a collection of C++ libraries that enables the use of finite difference and finite volume methods at a level that hides the details of the associated data structures, as well as the details of the parallel implementation. It is based on the A++/P++ array class library and is designed for solving problems on a structured grid or a collection of structured grids. In particular, it can use curvilinear grids, adaptive mesh refinement and the composite overlapping grid methods to represent problems with complex moving geometry. This paper introduces Overture, its motivation, and specifically the aspects of the design central to portability and high performance. In particular we focus on the mechanisms within Overture that permit a hierarchy of abstractions and those mechanisms which permit their efficiency on advanced serial and parallel architectures. We expect that these same mechanisms will become increasingly important within other object-oriented frameworks in the future.