The localization technique in equivariant cohomology is a powerful tool in many different fields, especially algebraic geometry, algebraic topology, symplectic geometry, algebraic combinatorics, and singularity theory. The first goal of this talk is to recall the localization formula in the theory of equivariant cohomology which was proved independently by Atiyah-Bott and Berline-Vergne in 1984. Then I will present an application to Schubert calculus on the Lagrangian Grassmannian. In particular, the Schubert structure constants in this case will be formulated.