Index and nullity of minimal surfaces

We discuss the strategies and results on the determination of index and nullity of minimal surfaces. In particular, we prove that for any large enough $m$, the genus $\gamma=m+1$ equator-poles minimal surface doubling of the equatorial two-sphere in the round three-sphere, which has two catenoidal bridges at the poles and  $m$ bridges equidistributed along the equatorial circle and was discovered in earlier work of Kapouleas, has index $2g+5=2m+7$ and nullity $6$.  We also discuss the progress in the study of indices of minimal surfaces from similar constructions.