In recent years, tissue engineering has achieved significant advancements towards the repair of damaged tissues. Until this day, the vascularization of engineered tissues remains a challenge to the development of large-scale artificial tissue. Recent breakthroughs in biomaterials and three-dimensional (3D) printing have made it possible to manipulate two or more biomaterials with complementary mechanical and/or biological properties to create hybrid scaffolds that imitate natural tissues. Hydrogels have become essential biomaterials due to their tissue-like physical properties and their ability to include living cells and/or biological molecules. Furthermore, 3D printing, such as dispensing-based bioprinting, has progressed to the point where it can now be utilized to construct hybrid scaffolds with intricate structures. Current bioprinting approaches are still challenged by the need for the necessary biomimetic nano-resolution in combination with bioactive spatiotemporal signals. Moreover, the intricacies of multi-material bioprinting and hydrogel synthesis also pose a challenge to the construction of hybrid scaffolds. This manuscript presents a brief review of scaffold bioprinting to create vascularized tissues, covering the key features of vascular systems, scaffold-based bioprinting methods, and the materials and cell sources used. We will also present examples and discuss current limitations and potential future directions of the technology.