  In this contribution we summarize our recent progress in understanding the
relation between ${\cal N} = 1$ superconformal indices and relativistic
elliptic integrable models. We start briefly reviewing the emergence of such
models in computations of the index in presence of surface defect. Next we give
an example of such relation considering $4d$ theories obtained in the
compactificaiton of $6d$ $(D_{N+3},D_{N+3})$ minimal conformal matter theories.
In this case we obtain van Diejen model as well as its higher rank
generalizations on $A_N$ and $C_2$ root systems. Finally we review a novel
algorithm for computation of the ground states of elliptic integrable systems
from superconformal indices that was recently proposed by us.
