Coherent x-rays have long been sought as a tool to discover microscopic details of physical and biological assemblies. Such radiation would permit biologists, chemists and physicists to probe with spatial resolutions better than 1,000 Å (perhaps 10 to 100 Å in special circumstances), and with an ability to distinguish concentrations of specific atomic elements. It has been the prevailing view that such radiation, when available, would emanate from an atomic x-ray laser. Although that is possible, we are coming to realize that to a large degree these needs will first be satisfied by coherent x-rays generated through the interaction of relativistic electron beams of very high brightness with periodic magnet structures (undulators). Within the next 2-5 years it will be possible with undulators and monochromators to generate x-rays at substantial peak and average powers, with thousands of wavelengths of longitudinal coherence, full spatial coherence, complete polarization control and broad tunability at megahertz repetition rates.