Abstract: We review briefly some results of the theory of elliptic hypergeometric functions - a new class of special functions of mathematical physics. We outline general structure of these functions, the elliptic beta integral (the most general univariate exact integration formula generalizing Euler's beta integral), an elliptic analogue of the Gauss hypergeometric function, its relation to the exeptional root system $E_7$, and the elliptic hypergeometric equation. A general survey of the subject is given here.