Diseases and injuries affecting tendons (Ts) and ligaments (Ls) are among the most frequently diagnosed musculoskeletal disorders. Although many of these are not life-threatening, they can cause severe debilitation, ultimately leading to substantial reductions in the patients’ mobility and quality of life. Even though the relevant advances in surgical and rehabilitative approaches to treat T/Ls diseases, the incidence of complications associated with those approaches is still too high, making T/Ls diseases an unmet clinical need. Currently, there is no consensus on an effective therapeutic strategy able to promote a complete T/Ls healing process. Over the past decade, there has been a growing interest in developing tissue-engineered tendon constructs as viable graft alternatives. In this review, we aim to delve into the latest advancements in the field of tissue engineering for tendon repair. The most advanced technologies such as electrospinning, 3D printing, melt electrowriting and hybrid fabrication techniques have been discussed, adopting critical connections with biological, and biomolecular aspects. Furthermore, this review provides comprehensive insights into current strategies, and future directions, of T/Ls regeneration using tissue engineering approaches, thus paving the way to the development of new effective approaches to T/Ls diseases.