An approach using polychromatic x-ray Laue diffraction is described for studying pressure induced microstructural changes of materials under pressure. The advantages of this approach with respect to application of monochromatic x-ray diffraction and other techniques are discussed. Experiments to demonstrate the applications of the method have been performed on the α → β phase transition in Si at high pressures using a diamond anvil cell. We present the characterization of microstructures across the α-β phase transition, such as morphology of both the parent and product phases, relative orientation of single-crystals, and deviatoric strains. Subtle inhomogeneous strain of the single-crystal sample caused by lattice rotations becomes detectable with the approach.