Recent advances in tissue engineering have adapted the additive manufacturing technology, also known as three-dimensional printing, which is used in several industrial applications, for the fabrication of bioscaffolds and viable tissue and/or organs to overcome the limitations of other in vitro conventional methods. 3D bioprinting technology has gained enormous attention as it enabled 3D printing of a multitude of biocompatible materials, different types of cells and other supporting growth factors into complex functional living tissues in a 3D format. A major advantage of this technology is its ability for simultaneously 3D printing various cell types in defined spatial locations, which makes this technology applicable to regenerative medicine to meet the need for suitable for transplantation suitable organs and tissues. 3D bioprinting is yet to successfully overcome the many challenges related to building 3D structures that closely resemble native organs and tissues, which are complex structures with defined microarchitecture and a variety of cell types in a confined area. An integrated approach with a combination of technologies from the fields of engineering, biomaterials science, cell biology, physics, and medicine is required to address these complexities. Meeting this challenge is being made possible by directing the 3D bioprinting to manufacture biomimetic-shaped 3D structures, using organ/tissue images, obtained from magnetic resonance imaging and computerized tomography, and employing computer-aided design and manufacturing technologies. Applications of 3D bioprinting include the generation of multilayered skin, bone, vascular grafts, heart valves, etc. The current 3D bioprinting technologies need to be improved with respect to the mechanical strength and integrity in the manufactured constructs as the presently used biomaterials are not of optimal viscosity. A better understanding of the tissue/organ microenvironment, which consists of multiple types of cells, is imperative for successful 3D bioprinting.