The magneto-electro-elastic (MEE) materials are able to effectively realize the mutual transformation among the electric energy, magnetic energy and mechanical energy. They are widely used in many important areas (e.g., in aerospace, biomedicine and intelligent manufacturing) due to their excellent properties. However, owing to low fracture toughness and high defect sensitivity, MEE materials are prone to crack. In this paper, we give a brief summary on fracture studies of MEE smart materials, mainly from analytical and numerical perspectives.