This article reviews the technical literature on the determination of a residual stress profile by successive extension of a slot and measurement of the resulting strains or displacements. This technique is known variously in the literature as the crack compliance method, the successive cracking method, the slotting method, and a fracture mechanics based approach. The article briefly summarizes the chronological development of this method and then, to facilitate more detailed review, defines the components that make up the method. The theory section of the article first considers forward method solutions including fracture mechanics, finite element, analytical, and body force methods. Then it examines inverse solutions, including incremental inverses and series expansions. Next, the article reviews all experimental applications of the crack compliance method. Aspects reviewed include the specimen geometry and material, the details of making the slot, the deformation measurement, and the theoretical solutions used to solve for stress. Finally, the article makes a brief qualitative comparison between crack compliance and other residual stress measurement methods. In many situations, the crack compliance method offers several advantages over other methods: improved resolution of residual stress variation with depth; the ability to measure both small and very large parts; measurement of stress intensity factor caused by residual stress; measurement of crack closure stresses; increased sensitivity over other material removal methods; and the ability to measure non-crystalline materials. This review article contains 77 references.