In view of this, Bourgain proposed an ambitious programme which came to be known as “The Ribe Programme”: to find explicit metric descriptions of the most important invariants of normed linear spaces. He himself kick-started the programme by characterising superreflexivity. A Banach space X is called superreflexive if every space whose finite-dimensional spaces embed uniformly well into X, must automatically be reflexive. Bourgain showed this holds precisely if the space does not contain copies of arbitrarily large binary trees. Needless to say the general aim of the Ribe programme is not merely to find metric equivalents of linear properties but to transfer the subtle and well-developed theory of normed spaces to the nonlinear setting, and in this broader sense the programme had been anticipated in a prescient paper of Johnson and Lindenstrauss, Within a decade or two the Ribe programme acquired an importance that would have been hard to predict at the outset, as the insights provided by the programme became powerful tools in the theory of algorithms and more recently in geometric group theory. Data sets often come equipped with a metric structure but rarely a linear one. For a number of central algorithmic problems the most effective procedure is to embed the data-set into a familiar linear geometry, without distorting it too much, and then use the linear structure to analyse the embedded copy of the data. Plainly, data that fail to possess a metric property that holds in the linear geometry cannot be embedded: so it is essential to understand what these properties are and where they appear. The study of groups as metric spaces and in particular their embeddability into simpler geometric structures has become a subject of intense interest in the last 5-10 years because of its connection with several famous problems such as the Novikov conjecture.