Dynamics of interval exchange transformations and translation flows

Interval exchange transformations (перекладывания), introduced by Oseledets, form an important class of measure-preserving systems. They are related to billiards (on polygons with rational angles) and to more general translation flows, and constitute one facet of what is called "Teichmueller dynamics". Among the mathematicians who made important contributions to this area were Katok, Keane, Rauzy, Masur, Veech, Zorich, Kontsevich, Avila, Forni, Eskin, Mirzakhani...
I will survey a (small) part of the rich theory of these systems, focusing on their spectral properties and symbolic realization (coding), built using Bratteli-Vershik (BV) diagrams. In particular, flows on random uniquely ergodic BV diagrams, constructed by A. Bufetov, will play a role.