While the uniaxial elongational viscosity is widely investigated, and its relevance for processing is described in the literature, much less has been published on the recoverable extensional flow of polymer melts. This paper presents a short overview of the dependencies of the recoverable elongation on the molecular structure of a polymer, and on some experimental parameters. Its main focus lies on the discussion of processing operations and applications that are largely affected by the elastic components of elongational flow. The recoverable portions of stretched films are considered, and the exploitation of the shrinkage of films, due to the recovery of frozen recoverable deformations, and its role for applications are addressed. The analysis of measurements of velocity fields in the entry region of a slit die and results on the determination of the recoverable elongation from uniaxial experiments, according to the literature, lead to the conclusion of dominant elastic extensions. Considering these facts, the assumptions for Cogswell’s widely used method of determining elongational viscosities under processing conditions from entrance flow are not realistic. As examples of a direct application of extrudate swell from short dies for processing, pelletizing and fused deposition modelling within additive manufacturing are addressed. The special features of extrudate swell from short dies, and uniaxial recoverable elongation for a polymer filled with rigid particles in comparison to an immiscible polymer blend, are presented and discussed.