This chapter is devoted to asymptotic behavior of transport and elastic properties of thin layers, which cover or join solid bodies. If the thin layer possesses transport or elastic characteristics compared to the characteristics of the solid bodies, it does not affect global transport / elastic properties of the structure. In this case, thin layers affect the characteristics of local nature, for example, the strength of the structure. In the case where the characteristics of the layers strongly differ from the characteristics of the bodies, one usually arrives at a limit problem with interface condition on the surface corresponding to the limit position of the thin layer. The rigorous asymptotic analysis of such problems started in [317, 337, 338], (see also bibliographical comment in [318]), which were followed by [42, 71, 87, 204, 229, 263, 289, 290].