Point defects, dislocations, grain boundaries and interfaces are always involved in ceramic microstructures and play important roles for physical and chemical properties of ceramics. Currently, proper control of these crystal defects is inevitable to tailor ceramic materials with superior properties. This article reviews recent research projects on distinct properties and phenomena in ceramics due to crystal defects. In particular, we would like to emphasize importance of central core regions of crystal defects, namely, "crystal defect cores". They have specific electronic and atomic structures that are different from those in bulk. Recent advances of nanoscale characterizations and theoretical calculations make it possible to acquire a variety of quantitative data on electronic structures enclosed at the crystal-defect cores, which gives clear understanding of various ceramic properties at the electronic and atomic levels.