Although brittle fracture in compression has been a subject of study since the pioneering work of Griffith, some fundamental aspects of the fracture mechanism and phenomenon still remain unclear. Further, computer simulations of fracture processes are rather limited. Thus, a review and summary of existing typical models and fracture criteria for brittle fracture in compression are provided. A sound fracture model should be established from knowledge of observed fracture behaviour and based on both a stress and an energy criterion.