As the number and variety of ceramic materials have grown so rapidly in the last few decades, ranging from silicon nitride structural ceramics to the perovskite superconductors to the ferroelectric oxides to semiconducting sensors, the number of scientific and technical issues has also grown rapidly. Many of the basic questions relate to the role the microstructures play in determining the observed physical behavior, but increasingly it is not the geometric properties of the microstructure that are of central concern but rather compositional variations and associated electrical characteristics.