  Robertson and Seymour constructed for every graph $G$ a tree-decomposition
that efficiently distinguishes all the tangles in $G$. While all previous
constructions of these decompositions are either iterative in nature or not
canonical, we give an explicit one-step construction that is canonical. The key
ingredient is an axiomatisation of 'local properties' of tangles.
Generalisations to locally finite graphs and matroids are also discussed.
