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In this contribution we summarize our recent progress in understanding therelation between ${\cal N} = 1$ superconformal indices and relativisticelliptic integrable models. We start briefly reviewing the emergence of suchmodels in computations of the index in presence of surface defect. Next we givean example of such relation considering $4d$ theories obtained in thecompactificaiton 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 rankgeneralizations on $A_N$ and $C_2$ root systems. Finally we review a novelalgorithm for computation of the ground states of elliptic integrable systemsfrom superconformal indices that was recently proposed by us.

Elliptic Integrable Models and Their Spectra from Superconformal Indices