Tendon injuries often heal slowly because of the limited vascularity, low cellularity, and low metabolic activity of native tendon tissue. Newly formed tendon tissue is frequently characterized by disorganized collagen alignment, reduced mechanical performance, and scar-like remodeling, making it difficult to restore the structure and function of native tendon. Bioprinting enables precise control over material composition, spatial architecture, fiber orientation, and the distribution of cells and bioactive components, thereby providing a promising strategy for functional tendon regeneration. However, tendon is a highly load-bearing and anisotropic tissue, whereas most hydrogel-based bioinks, despite their favorable cytocompatibility and cell-loading capacity, often remain biomechanically weak, with insufficient tensile strength, limited fatigue stability, and inadequate long-term shape fidelity, making them insufficient to independently meet the biomechanical requirements of tendon repair. This review summarizes natural and modified natural bioinks, synthetic reinforcing materials, printed load-bearing frameworks, and inorganic or ion-releasing functional components for tendon bioprinting, with emphasis on printability, biocompatibility, mechanical reinforcement, degradation behavior, and structural stability. We further discuss functional strategies involving structural and topographical modulation, bioactive molecule delivery, immunomodulatory regulation, physical stimulation, and smart responsiveness. Future studies should prioritize multi-material cooperative printing, tendon–bone interface gradient construction, responsive bioink development, long-term in vivo functional evaluation, and translational validation to advance tendon bioprinting materials toward functional regenerative applications.