3D bioprinting or additive manufacturing is an emerging innovative technology revolutionizing the field of biomedical applications by combining engineering, manufacturing, art, education, and medicine. This process involved incorporating the cells with biocompatible materials to design the required tissue or organ model in situ for various in vivo applications. Conventional 3D printing is involved in constructing the model without incorporating any living components, thereby limiting its use in several recent biological applications. However, this uses additional biological complexities, including material choice, cell types, and their growth and differentiation factors. This state‐of‐the‐art technology consciously summarizes different methods used in bioprinting and their importance and setbacks. It also elaborates on the concept of bioinks and their utility. Biomedical applications such as cancer therapy, tissue engineering, bone regeneration, and wound healing involving 3D printing have gained much attention in recent years. This article aims to provide a comprehensive review of all the aspects associated with 3D bioprinting, from material selection, technology, and fabrication to applications in the biomedical fields. Attempts have been made to highlight each element in detail, along with the associated available reports from recent literature. This review focuses on providing a single platform for cancer and tissue engineering applications associated with 3D bioprinting in the biomedical field.