A detailed review of various fractal models used in tribology is presented. The analysis of the models is based on the use of the Cantor–Borodich (C_B) profile and its modifications. This profile and related models may be studied analytically and, therefore, they provide us with tools for rigorous analysis of fractal approaches to description of surface roughness and corresponding contact problems. In turn, this allows us to present a critical review of current fractal approaches to tribology. It will be demonstrated that fractal dimension alone cannot give a full description of surface roughness, however, some of these models may reflect the multilevel hierarchical structure of real surface roughness. This review helps to avoid the repetition of common erroneous statements about the use of fractal concepts in tribology.

Living organisms, such as geckos and insects, exhibit excellent climbing ability on various complex surfaces due to the hair-like hierarchical adhesive systems of their attachment devices. Over the past few decades, an increased understanding of the mechanisms of multiscale hierarchical adhesion systems and the continual improvement of theoretical modeling have promoted the rapid advancement in the design and application of biomimetic artificial adhesives. The modeling of biomimetic artificial adhesives has been developed from simple structures to complex constructions with multilevel hierarchical properties. A review of advances in developing these contact mechanics models is presented here. Adhesion and friction models considering multiscale hierarchical structural forms are discussed, focusing on multiscale hierarchical models based on the development of the Cantor-Borodich profiles. Finally, the most recent developments in studies of artificial setae having spatula-like ends, both axisymmetric and non-axisymmetric, are reviewed.