  We give a full list of known $\mathcal{N}=1$ supersymmetric quantum field
theories related by the Seiberg electric-magnetic duality conjectures for
$SU(N), SP(2N)$ and $G_2$ gauge groups. Many of the presented dualities are
new, not considered earlier in the literature. For all these theories we
construct superconformal indices and express them in terms of elliptic
hypergeometric integrals. This gives a systematic extension of the related
Romelsberger and Dolan-Osborn results. Equality of indices in dual theories
leads to various identities for elliptic hypergeometric integrals. About half
of them were proven earlier, and another half represents new challenging
conjectures. In particular, we conjecture a dozen new elliptic beta integrals
on root systems extending the univariate elliptic beta integral discovered by
the first author.
