Many of the electronic properties of condensed matter systems (such as clusters of atoms, solids with long or short range order, amorphous and liquid metals) are governed by the local atomic arrangements around the probe site. One of the techniques that is particularly sensitive to the local environment is the hyperfine interaction between the electrons and the nucleus. Experimentally, the techniques have included nuclear magnetic resonance, electron spin resonance, Mossbauer spectroscopy, perturbed angular correlation, muon spin rotation and interaction within ion beams. Through these techniques, studies of the electronic properties have not only provided precise information of the electronic structure, but equally important information on local atomic structure and coordination have also emerged. It has been possible to understand, for example, local "ordering" in glasses, order-disorder transition, role of correlations and defects in high temperature superconductors, metal-insulator transition in expanded fluids, atomic structure in small metal clusters, diffusion and clustering of atoms on surfaces and other restricted geometries. These experiments measure quantities at precise positions in space and consequently, provide a critical test for the calculated electron eigenfunctions, structural models and low frequency dynamics. Development of new computational methods aided by high speed computers has helped theorists to meet this challenge, and fundamental understanding exists in many areas although much more needs to be done. These proceedings review the current status in our understanding of the hyperfine and other interactions that have enabled determination of the local atomic structure in a broad class of physical systems.