This paper discusses micropstructural aspects of brittleness fracture of polycrystalline materials caused by intergranular fracture. Structure-dependent intergranular brittle fracture in bicrystals and polycrystals are discussed and predicted theoretically. Experimental evidence for the structure-dependent intergranular fracture is shown and some general features are discussed to demonstrate the relationship between grain boundary structure/character, grain boundary energy and intergranular fracture strength. Theoretical prediction of the fracture toughness based on the strongest-link theory is introduced for polycrystals with different grain boundary microstructures, primarily defined by the grain boundary character distribution, grain boundary connectivity. Finally recent achievements of successful control of intergranular brittleness by grain boundary engineering based on the strongest-link theory are introduced for different materials.