Regenerative medicine offers the potential to repair or substitute defective tissues by constructing active tissues to address the scarcity and demands for transplantation. The method of forming 3D constructs made up of biomaterials, cells, and biomolecules is called bioprinting. Bioprinting of stem cells provides the ability to reliably recreate tissues, organs, and microenvironments to be used in regenerative medicine. 3D bioprinting is a technique that uses several biomaterials and cells to tailor a structure with clinically relevant geometries and sizes. This technique's promise is demonstrated by 3D bioprinted tissues, including skin, bone, cartilage, and cardiovascular, corneal, hepatic, and adipose tissues. Several bioprinting methods have been combined with stem cells to effectively produce tissue models, including adult stem cells, embryonic stem cells (ESCs), induced pluripotent stem cells (iPSCs), and differentiation techniques. In this review, technological challenges of printed stem cells using prevalent naturally derived bioinks (e.g., carbohydrate polymers and protein-based polymers, peptides, and decellularized extracellular matrix), recent advancements, leading companies, and clinical trials in the field of 3D bioprinting are delineated.