goes into the rubbing solids and may results in huge thermal gradients and very high localized temperatures at sliding asperities [@bowden_tabor; @rice2006heating]. These extreme thermo-mechanical loads can induce phase transformations and changes in material microstructures. (9) Local wear and initiation of fatigue cracks in fretting conditions [@proudhon2005ijf; @kubiak2011ti] strongly depend on the local stress state, which is intimately linked with the surface roughness. (10) Produced by adhesive wear [@sasada1984w], debris particles are necessarily related to the true contact area as discussed in (3); geometrical characteristics of surfaces are less important for the debris formed in abrasive wear [@hokkirigawa1988ti]. The presence of debris (or mobile third body) can significantly affect the true contact area and thus modify the kinetics of debris production. (11) Effect of the true contact area on the boundary lubrication is straightforward, concerning the hydrodynamic lubrication regimes and mixed lubrication the opening (gap) field plays an essential role and determines the film thickness, its possible breakage and thus determines the resulting friction and wear. In all the describing processes and phenomena the mechanical interaction between rough surfaces plays the key role. Accurate prediction of this mechanical interaction would allow constructing reliable and physically sound models for all the 