  General elliptic hypergeometric functions are defined by elliptic
hypergeometric integrals. They comprise the elliptic beta integral, elliptic
analogues of the Euler-Gauss hypergeometric function and Selberg integral, as
well as elliptic extensions of many other plain hypergeometric and
$q$-hypergeometric constructions. In particular, the Bailey chain technique,
used for proving Rogers-Ramanujan type identities, has been generalized to
integrals. At the elliptic level it yields a solution of the Yang-Baxter
equation as an integral operator with an elliptic hypergeometric kernel. We
give a brief survey of the developments in this field.
