It has been demonstrated, through theory and experiments, that compressive layers arrest large surface and internal cracks to produce a stress below which the material will not fail. This enables the materials to have a Threshold Strength. The stress intensity function, K, was derived for a crack sandwiched between two compressive layers. This function suggests that the threshold strength is proportional to the magnitude of the residual, compressive stress, the thickness of the compressive region, and inversely proportional to the distance between the compressive regions. All of these factors have been experimentally examined for laminar composites containing thin, compressive layers. Cracks that propagate straight though the layer obey the K function used to model this behavior. Crack bifurcation, which occurs at high compressive stresses, produces a larger threshold strength than predicted. Crack bifurcation is not fully understood. During the initial studies, differential thermal contraction during cooling from the densification temperature was used to develop the compressive stresses. A molar volume change to induce the compressive stress was also used to develop the compressive stresses. In one case, it was shown that the compressive stresses could arise when the compressive layer contained a material that underwent a structural phase transformation during cooling. In another, ion exchanged glass plates that are subsequently bonded together also produce a threshold strength. Factors that affect the threshold strength are reviewed.