  The univariate elliptic beta integral was discovered by the author in 2000.
Recently Bazhanov and Sergeev have interpreted it as a star-triangle relation
(STR). This important observation is discussed in more detail in connection to
author's previous work on the elliptic modular double and supersymmetric
dualities. We describe also a new Faddeev-Volkov type solution of STR,
connections with the star-star relation, and higher-dimensional analogues of
such relations. In this picture, Seiberg dualities are described by symmetries
of the elliptic hypergeometric integrals (interpreted as superconformal
indices) which, in turn, represent STR and Kramers-Wannier type duality
transformations for elementary partition functions in solvable models of
statistical mechanics.
