  We introduce and study the notion of relative rigidity for pairs $(X,\JJ)$
where 1) $X$ is a hyperbolic metric space and $\JJ$ a collection of quasiconvex
sets 2) $X$ is a relatively hyperbolic group and $\JJ$ the collection of
parabolics 3) $X$ is a higher rank symmetric space and $\JJ$ an equivariant
collection of maximal flats Relative rigidity can roughly be described as
upgrading a uniformly proper map between two such $\JJ$'s to a quasi-isometry
between the corresponding $X$'s.
  A related notion is that of a $C$-complex which is the adaptation of a Tits
complex to this context. We prove the relative rigidity of the collection of
pairs $(X, \JJ)$ as above. This generalises a result of Schwarz for symmetric
patterns of geodesics in hyperbolic space. We show that a uniformly proper map
induces an isomorphism of the corresponding $C$-complexes. We also give a
couple of characterizations of quasiconvexity. of subgroups of hyperbolic
groups on the way.
