Additive manufacturing has revolutionized science and technology, giving rise to the innovative field of bioprinting. Bioprinting, an extension of this revolution, has broad applications in creating functional tissues to replace damaged or diseased ones. The process involves printing live cells with biomaterials, integrating computer-aided design (CAD) and computer-aided manufacturing (CAM), which has become a significant technical challenge. The key focus is on achieving controlled cell distribution and high-resolution cell deposition within complex 3D tissues. This approach allows for precise fabrication and high reproducibility through automation, enabling efficient mass production on demand. Throughout the bioprinting process, bioinks-typically hydrogels containing biomaterials and specific cell types are used to construct tissue. These bioinks can be cross-linked or stabilized during or immediately after printing and may consist of natural or synthetic materials, either alone or in hybrid combinations. In some cases, bioinks can even be composed solely of cell aggregates without additional materials. This review provides an in-depth exploration of bioprinting technology, the Bio-CAD approach, and the various bioinks currently in use, while also offering insights into their future development.