The talk will begin with an brief overview of work by O. & J. Viro, V.Mazurovskii, S.Finashin on configurations of skew lines in Euclidean space R^3, and then will focus on a particular case of skew lines called rectangular (and square) weavings. These have recently been the subject of intensive research in Russia (most of it unpublished) by A.Skopenkov and others (including the lecturer). Square weavings have proved to be of interest to physicists, who like to regard them as random physical models and pose numerous very natural questions (most of which are unaswered) about them. Most of this stuff is unpublished, but here are references to four papers which give an idea of the flavor of the subject: [1] O.Viro, J.Drobotukhina, Configurations of skew lines, Leningrad Math.J., 1:4 (1989), 1027-1050. [2] V.Mazurovskii, Configurations of at most six lines in RP^3, Springer Lecture Notes, vol.1054 (1991), 354-371. [3] J.Drobotukhina, An analogue of the Jones polynomial for links in RP^3, Leningrad Math. J., 2:3 (1991), 613-630. [4] D.Repovs, A.Skopenkov, F.Spaggiari, A infinite sequence of non-realizable weavings, Discr.and Applied Math. (2004)