  Let $\{W_i\}_{i\in I}$ be a (redundant) sequence of subspaces each being
endowed with a weight $v_i$, and let $\mathcal{H}$ be the closed linear span of
the $W_i$'s, a composite Hilbert space. Provided that $\{(W_i,v_i)\}_{i \in I}$
satisfies a certain property which controls the weighted overlaps of the
subspaces, it is called a {\em fusion frame}. These systems contain
conventional frames as a special case, however they go far ``beyond frame
theory''. In case each subspace $W_i$ is equipped with a frame system
$\{f_{ij}\}_{j \in J_i}$ by which it is spanned, we refer to
$\{(W_i,v_i,\{f_{ij}\}_{j \in J_i})\}_{i \in I}$ as a {\em fusion frame
system}.
  In this paper, we describe a weighted and distributed processing procedure
that fuse together information in all subspaces $W_i$ of a fusion frame system
to obtain the global information in $\mathcal{H}$. The weighted and distributed
processing technique described in fusion frames is not only a natural fit in
distributed processing systems such as sensor networks, but also an efficient
scheme for parallel processing of very large frame systems. We further provide
an extensive study of the robustness of fusion frame systems.
