It is difficult to fabricate tubular-shaped tissues and organs (e.g., trachea, blood vessel, and esophagus tissue) with traditional biofabrication techniques (e.g., electrospinning, cell-sheet engineering, and mold-casting) because these have complicated multiple processes. In addition, the tubular-shaped tissues and organs have their own design with target-specific mechanical and biological properties. Therefore, the customized geometrical and physiological environment is required as one of the most critical factors for functional tissue regeneration. 3D bioprinting technology has been receiving attention for the fabrication of patient-tailored and complex-shaped free-form architecture with high reproducibility and versatility. Printable biocomposite inks that can facilitate to build tissue constructs with polymeric frameworks and biochemical microenvironmental cues are also being actively developed for the reconstruction of functional tissue. In this review, we delineated the state-of-the-art of 3D bioprinting techniques specifically for tubular tissue and organ regeneration. In addition, this review described biocomposite inks, such as natural and synthetic polymers. Several described engineering approaches using 3D bioprinting techniques and biocomposite inks may offer beneficial characteristics for the physiological mimicry of human tubular tissues and organs.