Many of the major challenges facing today's engineering science are related to miniaturization. In this field, vital progress can be made by studying Nature's solutions: Insects and other living creatures have solved many of the same problems during their evolution. Biological micro- and nanotribology aims to gather information about friction, adhesion and wear in such biological systems and to exploit this new knowledge, e.g. in the design of micro-electro- mechanical systems, the development of novel types of monolayer lubrication, the invention of new adhesives, and the construction of artificial joints. By employing a combination of approaches from several disciplines -- physics, engineering, tribology, biology, and materials science -- the authors elucidate the principles of a variety of biomechanical systems that rely on frictional surfaces or adhesive secretions to attach parts of the body to one another or to attach organisms to a substrate. This account provides an excellent starting point for engineers and physicists working with biological systems and for biologists studying friction and adhesion. It will also serve as a valuable introduction for graduate students entering this interdisciplinary field of research.