  We construct and analyse models of equivariant cohomology for differentiable
stacks with Lie group actions extending classical results for smooth manifolds
due to Borel, Cartan and Getzler. We also derive various spectral sequences for
the equivariant cohomology of a differentiable stack generalising among others
Bott's spectral sequence which converges to the cohomology of the classifying
space of a Lie group.
