Melt spinning of polymer melts is a formation process making extremely high demands on the material＇s continuous deformation ability by highest deformation speeds. The structural conditions of a thermoplastic polymer which are necessary for spinnability have not been exactly cleared up yet. But this knowledge gap must be closed especially with regard to the many efforts to spin fibers with new properties made from modified polymers of polymer blends. The article is begun with a pragmatic definition of the spinnability of a polymer melt. The discussion of a structural rheological model shows a correlation between dynamic rheological measurement datas of polymer melts and experimental experience about their spinnability. Proceeding from a comprehensive description of possible failure cases (fiber beak problems), results of rheological measurement of a number of different polymers, which are spinnable well, not as well or not at all, are compared. The article is concluded by some comments on open problems which have to be solved by basic research in the near future.