The unsplittable flow problem is a variant of the normal ("fractional") flow problem where the flow from the source to any terminal must all be along a single path. It combines two fundamental network problems: routing (finding good paths for network traffic), and packing (combining multiple paths in a single network while respecting capacity constraints). As a generalization of both the disjoint paths problem and bin packing, it is NP-complete. Until recently, no good approximation algorithms for unsplittable flow problems were known. In this talk, we will describe recent work by Jon Kleinberg (presented at FOCS 96) which provides constant-factor approximations for several single-source multiple-sink unsplittable flow problems. We will also consider some generalizations to the multiple source case.