  Localization principle is a powerful analytic tool in supersymmetric gauge
theories which enables one to perform supersymmetric path integrals explicitly.
Many important formulae have been obtained, and they led to a major
breakthrough in the understanding of gauge theories at strong coupling as well
as the dynamics of branes in M-theory. Some of those results are reviewed,
focusing especially on Pestun's solution to four-dimensional N=2 supersymmetric
gauge theories on S^4 and the subsequent developments on three or
four-dimensional gauge theories on spheres.
