Atomic motions and, especially, correlations in atomic motion over angstrom length scales are a sensitive probe of material properties: phonons in single crystals respond to the detailed interactions between atoms, including both short- and long-range forces, and screening thereof, while the atomic dynamics of liquids is intimately connected with nearly all aspects of liquid behavior. Scientific questions associated with measuring dynamics include the detailed nature of phase transitions, correlations of atomic motions with electronic or magnetic properties (superconductivity, ferro-electric behavior, magnetoelastic coupling, etc.), and also very practical issues, such as investigating elasticity. Not surprisingly, both from the point of view of basic science and for applications such as geology, there is strong desire to extend studies of atomic dynamics throughout material phase diagrams, into extreme conditions.