In this talk we consider the unsplittable Flow problem (UFP): given a directed or undirected network G=(V,E) with edge capacities and a set of terminal pairs (or requests) with associated demands, find a subset of the pairs of maximum total demand for which a single flow path can be chosen for each pair so that for every edge, the sum of the demands of the paths crossing the edge does not exceed its capacity. We study the UFP both in the offline (all requests are given from the beginning) and the online (requests arrive at the system one after the other) setting. For this we introduce a new graph parameter, the flow number. With the help of the flow number we develop a general method for transforming arbitrary multicommodity flow solutions into solutions that use short paths only, generalizing a theorem of Leighton and Rao. Both the parameter and the method may therefore be of independent interest. They allow us to prove upper bounds on the approximation ratio and competitive ratio of algorithms for the UFP that are significantly below all previous upper bounds.