Finite deformation contact problems with frictional effects and finite shape changes due to wear are investigated. To capture the finite shape changes, a third configuration besides the well-known reference and spatial configurations is introduced, which represents the time-dependent worn state. Consistent interconnections between these states are realized by an arbitrary Lagrangean-Eulerian formulation. The newly developed partitioned and fully implicit algorithm is based on a Lagrangean step and a shape evolution step. Within the Lagrangean step, contact constraints as well as the wear equations are weakly enforced following the well-established mortar framework. Additional unknowns due to the employed Lagrange multiplier method for contact constraint enforcement and due to wear itself are eliminated by condensation procedures based on the concept of biorthogonality and the so-called dual shape functions. Several numerical examples in both 2D and 3D are provided to demonstrate the performance and accuracy of the proposed numerical algorithm. Copyright © 2016 John Wiley & Sons, Ltd.