  The real singular cohomology ring of a homogeneous space $G/K$, interpreted
as the real Borel equivariant cohomology $H^*_K(G)$, was historically the first
computation of equivariant cohomology of any nontrivial connected group action.
After early approaches using the Cartan model for equivariant cohomology with
real coefficients and the Serre spectral sequence, post-1962 work computing the
groups and rings $H^*(G/K)$ and $H^*_H(G/K)$ with more general coefficient
rings motivated the development of minimal models in rational homotopy theory,
the Eilenberg-Moore spectral sequence, and A-infinity algebras.
  In this essay, we survey the history of these ideas and the associated
results.
