  We consider Seiberg electric-magnetic dualities for 4d $\mathcal{N}=1$ SYM
theories with SO(N) gauge group. For all such known theories we construct
superconformal indices (SCIs) in terms of elliptic hypergeometric integrals.
Equalities of these indices for dual theories lead both to proven earlier
special function identities and new conjectural relations for integrals. In
particular, we describe a number of new elliptic beta integrals associated with
the s-confining theories with the spinor matter fields. Reductions of some
dualities from SP(2N) to SO(2N) or SO(2N+1) gauge groups are described.
Interrelation of SCIs and the Witten anomaly is briefly discussed. Possible
applications of the elliptic hypergeometric integrals to a two-parameter
deformation of 2d conformal field theory and related matrix models are
indicated. Connections of the reduced SCIs with the state integrals of the knot
theory, generalized AGT duality for (3+3)d theories, and a 2d vortex partition
function are described.
