Among various severe plastic deformation (SPD) techniques, constrained groove pressing (CGP) has arisen as a famous technique for fabricating ultrafine-grained sheet metals and alloys in recent times. The severe strain is applied to improve the mechanical performance and properties. However, inhomogeneous grain refinement, lower formability, surface unevenness, and microcracks are the common limitations of conventional CGP-processed samples. Therefore, this review inspects the latest progress through modifications of the CGP process and compares the process efficacy with the conventional process. Advanced CGP processing techniques, such as modification of die design, annealing of the processed sample, cross CGP, ring CGP, hybrid SPD, covered sheet casing CGP, and rubber pad CGP, are emerging techniques to up-scale the procedure and improve the grain refinement and thereby produce superior mechanical properties. In this review paper, the historic research of conventional CGP and its effect on grain refinement and mechanical properties is initially briefed and then recent progress through different advanced techniques is highlighted, especially in alloys. Albeit significant progress has been observed in CGP, the future scope and successful usage of CGP-processed samples in actual practice are discussed in the last stage.