We provide a review of recent works about the Coupled Criterion (CC), originally developed to assess the initiation of a crack and thus overcome a main limitation of linear elastic fracture mechanics. This paper includes theoretical and implementation aspects of the CC, new fundamental developments such as extensions to 3D, dynamic aspects, nonlinearities or fatigue. It also focuses on confrontations between the CC and other fracture modeling approaches such as cohesive zone models or phase field approach for fracture. Originally developed in 2D, for linear elastic materials under the assumption of small deformations, the CC has now expanded and can be applied to a wide range of applications from macroscopic to atomic scale.