Modern high-performance computers are now capable of calculations that can be used to determine the preferred atomic arrangements in complex systems. Both first-principles and semiempirical approaches have been developed with complementary capabilities. At the same time, powerful transmission electron microscopes have been developed that yield direct atomic-scale images of crystals and extended defects such as dislocations, grain boundaries and buried interfaces. This paper presents several examples where a synergistic approach combining theoretical results, Z-contrast scanning transmission electron microscopy, and spatially resolved electron energy loss spectroscopy (EELS) have led to the elucidation of complex atomic structures. In some cases, theory predicts, experiment confirms and expands and theory revisits; in other cases, observations come first and theory helps put together a comprehensive picture or goes beyond the original observations with new predictions. In both cases, equilibrium structures, impurity or stressinduced structural transformations, and dynamical processes such as diffusion, segregation or precipitation are elucidated in great detail.