  Equivariant $K$-theory is a generalized equivariant cohomology theory which
is a hybrid of the $K$-theory of a topological space and the representation
theory of the group acting on it. In this article, we review the basics of
equivariant $K$-theory and focus on the localization theorem and formula due to
Atiyah and Segal, which have become important tools in equivariant topology
nowadays. We then discuss the application of equivariant $K$-theory to
equivariant formality, and briefly mention some recent developments.
