Boundary value problems involving contact are important for industrial applications in both mechanical and civil engineering, such as structural foundations, bearings, metal forming processes, rubber sealings, drilling problems, crash analysis of cars, rolling contact between car tyres and the road, cooling of electronic devices, and many more. Other applications are related to biomechanical engineering design, where human joints, implants or teeth are considered. Due to this variety, contact problems today are combined either with large elastic or inelastic deformations, including time-dependent responses. Thermal coupling may also have to be considered, and even stability behaviour has to be linked to contact, such as wrinkling arising in metal forming problems.