In the first part, I will review the action of current algebras on cohomology of quiver varieties and an algebraic counterpart of this action on the center of quiver Hecke algebras, and state an isomorphism between the cohomology and the center (based on a joint work with Varagnolo-Vasserot). In the second part, I will explain a variation of this isomorphism and a relationship with the Coulomb branches recently introduced by Braverman-Finkelberg-Nakajima.