V.Meshkov Classification of textile structures By textile structures we mean double periodic links (interlacings). Such links can be considered as virtual links of genus~1. But because of their obvious practical importance textile structures are worth of special studying. Some issues around the classification problem for textile structures are discussed including the auxiliary problem of $k$-tangles enumeration, and Kauffman-type invariant for doubly periodic structures. This is a joint work with A.Bogdanov, A.Omelchenko, and M.Petrov.