We use localization and the Seiberg-Witten curve to exactly compute supersymmetric observables
in different ${\cal N}=2$ four-dimensional theories.
We first consider ${\cal N}=2$ SQCD with gauge group $SU(2)$ and two massive flavors.
We compute the exact free energy, including all instanton contributions, and show that the theory undergoes a
second-order quantum phase transition at a critical coupling.
In the second part, we use localization to compute large $N$ correlation functions in superconformal field theories.