This article introduces the concepts of linear-elastic fracture mechanics (LEFM) and elastic-plastic fracture mechanics (EPFM). It reviews the fracture mechanics of ceramics and ceramic matrix composites (CMCs). The article describes some fracture toughness measurement techniques used on ceramics and CMCs: single edge notch bending, compact tension, double cantilever beam testing, chevron notch methods, and double torsion. It presents descriptions organized by their specimen types, and includes the advantages and disadvantages, as well as the experimental control schemes employed for each specimen type.