Tendon and ligament injuries caused by trauma and degenerative diseases are frequent and affect diverse groups of the population. Such injuries reduce musculoskeletal performance, limit joint mobility, and lower people's comfort. Currently, various treatment strategies and surgical procedures are used to heal, repair, and restore the native tissue function. However, these strategies are inadequate and, in some cases, fail to re‐establish the lost functionality. Tissue engineering and regenerative medicine approaches aim to overcome these disadvantages by stimulating the regeneration and formation of neotissues. Design and fabrication of artificial scaffolds with tailored mechanical properties are crucial for restoring the mechanical function of tendons. In this review, the tendon and ligament structure, their physiology, and performance are presented. On the other hand, the requirements are focused for the development of an effective reconstruction device. The most common fiber‐based scaffolding systems are also described for tendon and ligament tissue regeneration like strand fibers, woven, knitted, braided, and braid‐twisted fibrous structures, as well as electrospun and wet‐spun constructs, discussing critically the advantages and limitations of their utilization. Finally, the potential of multilayered systems as the most effective candidates for tendon and ligaments tissue engineering is pointed out.