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 at
omic structure can be slightly different from the crystal structure due to
substitutional disorder or strong electron-lattice coupling. In order to un
derstand the properties of such a system, it is more important to determine
the local atomic structure than the average crystal structure since the pr
operties 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 determinati
on, the pulsed neutron atomic pair-density function (PDF) analysis, and dem
onstrate how it helps us to understand the microscopic interactions in the
colossal magnetoresistive (CMR) manganites, ferroelectric oxides, and super
conductive 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 supercon
ductivity.