The complexities of compression failure are defined in terms of the three well known failure modes: yielding, cone failure, and axial splitting. The notion of compressive strength is shown to be useful only in the case of yielding. For compression cracking, where the stress at failure varies with geometry and manner of force application, compressive strength is not such a useful parameter. Therefore, new failure criteria are suggested for compression cracking based on the energy balance theory of fracture. These criteria explain why the force required for failure depends on the mode of cracking, on the fracture surface energy of the material, and on the geometry and elasticity of the specimen. Fracture surface energy, and not strength, is found to be the fundamental material property dictating compression cracking. These ideas are verified by detailed theoretical and experimental investigation of compression splitting in glassy materials. In particular, the effects of size on compression failure are interpreted, both platen and specimen dimensions influencing the fracture force. It is further shown that the mode of failure can change from brittle to ductile under certain conditions, for example, as the platens are widened or as the sample is reduced in size. Finally, the inhibiting effect of lateral forces on compression cracking is explained.