In the additive manufacturing method known as 3D bioprinting, living cells and nutrients are joined with organic and biological components to produce synthetic structures that resemble natural human tissues. To put it another way, bioprinting is a type of 3D printing that can create anything from bone tissue and blood vessels to living tissues for a range of medical purposes, including tissue engineering and drug testing and discovery. During the bioprinting process, a solution of a biomaterial or a mixture of several biomaterials in the hydrogel form, usually encapsulating the desired cell types, which are termed as bioink, is used for creating tissue constructs. This bioink can be cross-linked or stabilised during or immediately after bioprinting to generate the designed construct's final shape, structure, and architecture. This report thus offers a comprehensive review of the 3D bioprinting technology along with associated 3D bioprinting methods including ink-jet printing, extrusion printing, stereolithography, laser-assisted bioprinting and microfluidic techniques. We also focus on the types of materials, cell source, maturing, the implant of various representative tissue and organs, including blood vessels, bone and cartilage as well as recent advancements related to 3D bioprinting technology.