  The enumerative theory of simplicial subdivisions (triangulations) of
simplicial complexes was developed by Stanley in order to understand the effect
of such subdivisions on the $h$-vector of a simplicial complex. A key role
there is played by the concept of a local $h$-vector. This paper surveys some
of the highlights of this theory and some recent developments, concerning
subdivisions of flag homology spheres and their $\gamma$-vectors. Several
interesting examples and open problems are discussed.
