The fracture mechanical free discontinuity problem can be associated with a generalized, variational approach of GRIFFITH’s fracture theory. By introducing a regularization for the sharp displacement discontinuity at cracks and crack surfaces, stable computational fracture models are developed, e.g., the phase-field fracture formulation and the eigenfracture approach. The presented work summarizes recent findings regarding unrealistic deformation kinematics at cracks predicted by conventional formulations of both models and introduces the variational framework of Representative Crack Element to overcome these discrepancies. Illustrative examples for crack propagation and post-fracture behavior at small and finite deformations, brittle and cohesive failure as well as for rate-dependent materials frictional crack contact demonstrate the flexibility and the generality of the introduced Representative Crack Element.