The crystal structure determined by diffraction analysis is usually used as a basis for explaining the properties of a solid in terms of the nature of the atomic bonding. However, in many transition-metal oxides the actual atomic structure can be slightly different from the crystal structure due to substitutional disorder or strong electron-lattice coupling. In order to understand the properties of such a system, it is more important to determine the local atomic structure than the average crystal structure since the properties tend to reflect more strongly the local structure than the average structure. Recently local structural determination became much easier and more accurate due to the advent of synchrotron-based radiation sources. In this chapter we describe one of the methods of local structural determination, the pulsed neutron atomic pair-density function (PDF) analysis, and demonstrate how it helps us to understand the microscopic interactions in the colossal magnetoresistive (CMR) manganites, ferroelectric oxides, and superconductive cuprates. In particular, we show how the knowledge of the local structure leads to the concept of a critical stability of lattice polarons that controls the CMR phenomenon and possibly the high-temperature superconductivity.