  We give a brief review of the main results of the theory of elliptic
hypergeometric functions -- a new class of special functions of mathematical
physics. We prove the most general univariate exact integration formula
generalizing Euler's beta integral, which is called the elliptic beta integral.
An elliptic analogue of the Gauss hypergeometric function is constructed
together with the elliptic hypergeometric equation for it. Biorthogonality
relations for this function and its particular subcases are described. We list
known elliptic beta integrals on root systems and consider symmetry
transformations for the corresponding elliptic hypergeometric functions of the
higher order.
