Amorphous x-ray diffraction is used to obtain structural information on amorphous solids and liquids at high pressure as well as other materials without long range crystalline order including biologically important macromolecules and nanomaterials. The intense x-ray beams provided by synchrotron sources are ideal for diffraction studies of noncrystalline materials. We illustrate this with studies of the transition between low- and high-density forms of amorphous Si in the diamond anvil cell at high pressure, and the compressibility of amyloid fibrils.