3D printed/bioprinted tissue constructs are utilized for the regeneration of damaged tissues and as in vitro models. Most of the fabricated 3D constructs fail to undergo functional maturation in conventional in vitro settings. There is a challenge to provide a suitable niche for the fabricated tissue constructs to undergo functional maturation. Bioreactors have emerged as a promising tool to enhance tissue maturation of the engineered constructs by providing physical/biological cues along with a controlled nutrient supply under dynamic in vitro conditions. Bioreactors provide an ambient microenvironment most appropriate for the development of functionally matured tissue constructs by promoting cell proliferation, differentiation, and maturation for transplantation and drug screening applications. Due to the huge cost and limited availability of commercial bioreactors, there is a need to develop strategies to make customized bioreactors. Additive manufacturing (AM) may be a viable tool to fabricate custom designed bioreactors with better efficiency and at low cost. In this review, we have extensively discussed the importance of bioreactors in functionalizing tissue engineered/3D bioprinted scaffolds for bone, cartilage, skeletal muscle, nerve, and vascular tissue. In addition, the importance and fabrication of customized 3D printed bioreactors for the maturation of tissue engineered constructs are discussed in detail. Finally, the current challenges and future perspectives in translating commercial and custom 3D printed bioreactors for clinical applications are outlined.