Identifiable regions of high connectivity in a matroid or graph are captured by the notion of ``tangles''. For a tangle of order $k$ in a matroid or graph that satisfies a certain robustness condition, we describe a tree decomposition of the matroid or graph that displays, up to a certain natural equivalence, all of the $k$-separations of the matroid or graph that are non-trivial with respect to the tangle. This is joint work with Geoff Whittle.