Summary: We present the first implicit computational framework for simulating crack propagation along contact interfaces and surfaces under load in three-dimensional bodies, which is distinct from modelling the contact interaction associated with crack closure. We restrict ourselves to brittle fracture and frictionless contact and focus on numerical challenges associated with the coupling of unilateral constraints emerging from the Griffith’s criterion and the contact conditions. The formulation is based on the configurational mechanics framework and is solved using the finite element method. The approach utilises a monolithic Arbitrary Lagrangian-Eulerian formulation permitting simultaneous resolution of crack propagation and unilateral contact constraints. Contact is embedded in the model using the well-known mortar contact formulation. Evolving cracks are explicitly modelled as displacement discontinuities within the mesh. Heterogeneous approximation of arbitrary order is used to discretise spatial displacements, enabling \(hp\)-adaptive refinement around the crack front and the contact interfaces traversed by the crack. The result is a holistic approach which handles issues associated with thermodynamic consistency, numerical accuracy and robustness of the computational scheme. Several numerical examples are presented to verify the model formulation and implementation; they also highlight how contact pressure and load applied on surfaces traversed by cracks influence their propagation. The robustness of the approach is validated by comparison of our simulations with existing numerical results and an industrial experiment involving cracks of complex morphologies propagating along contact interfaces between multiple deformable bodies.