A review on SUSY gauge theories on $S^3$

This is the 9th article in the collection of reviews “Exact results on N=2 supersymmetric gauge theories”, ed. J.Teschner. We review the exact computations in 3D N=2 supersymmetric gauge theories on the round or squashed $S^3$ and the relation between 3D partition functions and 4D superconformal indices.