Picosecond and nanosecond transient structures have been observed directly using time-resolved X-ray diffraction and absorption. These experiments provide insight on the evolution of transient molecular structure on the atomic length scale during the course of a chemical reaction. Recent advances in the generation of short X-ray pulses and detectors have made time-resolved X-ray studies a reality. We discuss a few of the vast number of possible time-resolved structure studies in solids and fluids. Ultrafast relaxation dynamics of crystal lattice structures induced by picosecond and nanosecond laser pulses have been observed by means of time-resolved picosecond and nanosecond X-ray diffraction. Lattice deformation with 10 ps and 10(-3) Angstrom resolution have been performed. The picosecond X-ray system, which we have used, is described, and its application to time-resolved ultrafast X-ray diffraction in crystals and EXAFS in liquids is discussed.