Human body tissues such as muscle, blood vessels, tendon/ligaments, and nerves have fiber‐like fascicle morphologies, where ordered organization of cells and extracellular matrix (ECM) within the bundles in specific 3D manners orchestrates cells and ECM to provide tissue functions. Through engineering cell fibers (which are fibers containing living cells) as living building blocks with the help of emerging “bottom‐up” biomanufacturing technologies, it is now possible to reconstitute/recreate the fiber‐like fascicle morphologies and their spatiotemporally specific cell‐cell/cell‐ECM interactions in vitro, thereby enabling the modeling, therapy, or repair of these fibrous tissues. In this article, a concise review is provided of the “bottom‐up” biomanufacturing technologies and materials usable for fabricating cell fibers, with an emphasis on electrospinning that can effectively and efficiently produce thin cell fibers and with properly designed processes, 3D cell‐laden structures that mimic those of native fibrous tissues. The importance and applications of cell fibers as models, therapeutic platforms, or analogs/replacements for tissues for areas such as drug testing, cell therapy, and tissue engineering are highlighted. Challenges, in terms of biomimicry of high‐order hierarchical structures and complex dynamic cellular microenvironments of native tissues, as well as opportunities for cell fibers in a myriad of biomedical applications, are discussed.