We give an acount of the notion of hyperbolicity as defined by Gromov in the context of path-metric spaces. We prove the equivalence of five formulations of this notion, including the existence a linear isoperimetric function. We show that any set of $ n $ points in such a space can be approximated up to an additive constant, logrithmic in $ n $, by an immersed tree. We also show that the notion of hyperbolicity propagates, in the sense that a coarsly simply connected path-metric space which is hyperbolic on every ball of a given radius is globally hyperbolic --- provided the various constants are properly quanified.
in ``Group theory from a geometrical viewpoint'' (ed. E. Ghys, A. Haefliger, A. Verjovsky), World Scientific (1991) 64-167.