The physical sciences have increasingly demonstrated a significant influence on the life sciences. Engineering in particular has shown its input through the development of novel medical devices and processes having significance to the biomedical field. This review introduces and discusses several fiber generation protocols, which have recently undergone development and exploration for directly handling living cells from which continuous cell-bearing or living threads to scaffolds and membranes have been fabricated. In doing so these protocols have not only demonstrated their versatility but also opened several unique possibilities for the use of these scaffolds in a plethora of biological and medical applications. In particular, these living fibrous structural units could be explored for regeneration purposes, e.g., from accelerated wound healing to combating a wide range of pathologies when coupled with gene therapy. Thus, "living entities" such as these scaffolds could be most useful in surgery/medicine, including its exploration with stem cells for the preparation of unspecialized living scaffolds and membranes.