X-ray and neutron diffraction have been two key techniques for structural characterization of materials since their inception. If single crystals of the materials of interest cannot be synthesized, one has to resort to powder diffraction. This results in the loss of three-dimensional orientation information of the crystal, and one has to contend with the one-dimensional information that is inherent to powder diffraction, making it harder to analyze the data. The structural study of contemporary materials and their remarkable properties is a challenging problem, particularly when properties of interest result from interplay of multiple degrees of freedom. Very often these are associated with structural defects or relate to different length scales in a material. The signature of the defect-related phenomenon is visible as diffuse scattering in the diffraction pattern, and the signals associated with diffuse scattering are orders of magnitude smaller than Bragg scattering. Given these limitations, it is crucial to have high-resolution and high-intensity data along with the ability to carry out theoretical interpretation that goes beyond periodic lattice formalism of crystallography. Great advances have been achieved due to the advent of synchrotron and neutron sources, along with the availability of high-speed computational algorithms allowing materials scientists to work with a very small amount of sample (both single crystal and powder) and analyze vast amounts of data to unravel detailed structural descriptions that were not previously possible. This article presents some of these great advances in using scattering probes for materials characterization.