  We give a self-contained introduction to the theory of secondary polytopes
and geometric bistellar flips in triangulations of polytopes and point sets, as
well as a review of some of the known results and connections to algebraic
geometry, topological combinatorics, and other areas.
  As a new result, we announce the construction of a point set in general
position with a disconnected space of triangulations. This shows, for the first
time, that the poset of strict polyhedral subdivisions of a point set is not
always connected.
