  This paper gives an exposition of the authors' harmonic deformation theory
for 3-dimensional hyperbolic cone-manifolds. We discuss topological
applications to hyperbolic Dehn surgery as well as recent applications to
Kleinian group theory. A central idea is that local rigidity results (for
deformations fixing cone angles) can be turned into effective control on the
deformations that do exist. This leads to precise analytic and geometric
versions of the idea that hyperbolic structures with short geodesics are close
to hyperbolic structures with cusps. The paper also outlines a new harmonic
deformation theory which applies whenever there is a sufficiently large
embedded tube around the singular locus, removing the previous restriction to
cone angles at most 2pi.
