The fast-developing field of 3D bio-printing has been extensively used to improve the usability and performance of scaffolds filled with cells. Over the last few decades, a variety of tissues and organs including skin, blood vessels, and hearts, etc., have all been produced in large quantities via 3D bio-printing. These tissues and organs are not only able to serve as building blocks for the ultimate goal of repair and regeneration, but they can also be utilized as in vitro models for pharmacokinetics, drug screening, and other purposes. To further 3D-printing uses in tissue engineering, research on novel, suitable biomaterials with quick cross-linking capabilities is a prerequisite. A wider variety of acceptable 3D-printed materials are still needed, as well as better printing resolution (particularly at the nanoscale range), speed, and biomaterial compatibility. The aim of this study is to provide expertise in the most prevalent and new biomaterials used in 3D bio-printing as well as an introduction to the associated approaches that are frequently considered by researchers. Furthermore, an effort has been made to convey the most pertinent implementations of 3D bio-printing processes, such as tissue regeneration, etc., by providing the most significant research together with a comprehensive list of material selection guidelines, constraints, and future prospects.