Polychromatic microdiffraction is an emerging materials-characterization tool made practical by powerful X-ray and neutron sources, and by advanced optics and software. With polychromatic techniques, local crystalline properties including phase, texture (orientation), elastic strain, and defect density can be mapped with submicron spatial resolution in three dimensions. Here, we describe the evolving ability to nondestructively map local crystal structure in three dimensions and discuss how future advances will help address long-standing issues of inhomogeneous grain growth, deformation, fracture, and elastic strain. Current and future applications impact virtually all materials including electronic, solar, and light-emitting-diode (LED) materials, nanomaterials, structural materials, and joining materials. In addition, the ability to focus small beams on small samples dramatically increases signal-to-noise and greatly reduces the cost for extreme environmental chambers required for high-pressure, high-temperature, high-magnetic field or corrosive environments. Polychromatic techniques efficiently use source brilliance and minimize the required sample volume, which is essential for hard-to-make materials, irreplaceable materials, and for radioactive, toxic, or otherwise dangerous materials. New polychromatic neutron capabilities will significantly extend the range of samples that can be studied with neutrons and presents important new scientific opportunities for studies of magnetic materials, low Z elements, fragile crystal structures, and small samples in extreme environments.