X-ray and neutron diffraction are the most powerful methods for studying the structures of crystalline solids, including materials of importance to nuclear weapons and environmental programs. Crystallographically disordered solids are some of the most technologically useful materials due to their inherent disorder and high surface areas. Unfortunately, existing crystallographic methods are largely restricted to analyzing ordered materials, and disordered materials cannot be accurately characterized or modeled. We have developed a new method for diffraction analysis of the structural details of disordered materials. The method combines Rietveld refinement methods with a new treatment of disorder that completely describes scattering over all of reciprocal space sampled in a diffraction experiment. This approach has been applied to the common clay minerals but can be equally well applied to other disordered materials, such as zeolite catalysts, superconductors, and nanocomposites, representing a major breakthrough in our abilities to understand the structures of polycrystalline disordered materials.