Polymer melts are dense liquids of polymers. For short chains the physics is well described by the Rouse model, which regards polymers as chains of non-interacting beads connected by harmonic springs. For longer chains life becomes much more interesting. Chains above a certain length becomes topologically entangled with each other. This means that a single polymer can perform thermal fluctuations inside a tube along its coarse contour, since topological entanglements neighbouring chains limits the space available for thermal fluctuations.It also has the interesting result that each chain can only diffuse along its own contour, and relax stress via the two ends in a dynamics called reptation. During reptation the chain diffuses backwards and forwards inside its tube, each time the chain pokes it "head" or "tail" outside the tube, new tube is formed at one end while the old tube is forgotten at the other end. The memory function of the deformed tube structure is when determines the complex stress-relaxation response of viscoelastic polymer liquids.