  This is a survey of the $cd$-index of Eulerian partially ordered sets. The
$cd$-index is an encoding of the numbers of chains, specified by ranks, in the
poset. It is the most efficient such encoding, incorporating all the affine
relations on the flag numbers of Eulerian posets. Eulerian posets include the
face posets of regular CW spheres (in particular, of convex polytopes),
intervals in the Bruhat order on Coxeter groups, and the lattices of regions of
oriented matroids. The paper discusses inequalities on the $cd$-index,
connections with other combinatorial parameters, computation, and algebraic
approaches.
