Bioprinting is the assembly of three‐dimensional (3D) tissue constructs by layering cell‐laden biomaterials using additive manufacturing techniques, offering great potential for tissue engineering and regenerative medicine. Such a process can be performed with high resolution and control by personalized or commercially available inkjet printers. However, bioprinting's clinical translation is significantly limited due to process engineering challenges. Upstream challenges include synthesis, cellular incorporation, and functionalization of “bioinks,” and extrusion of print geometries. Downstream challenges address sterilization, culture, implantation, and degradation. In the long run, bioinks must provide a microenvironment to support cell growth, development, and maturation and must interact and integrate with the surrounding tissues after implantation. Additionally, a robust, scaleable manufacturing process must pass regulatory scrutiny from regulatory bodies such as U.S. Food and Drug Administration, European Medicines Agency, or Australian Therapeutic Goods Administration for bioprinting to have a real clinical impact. In this review, recent advances in inkjet‐based 3D bioprinting will be presented, emphasizing on biomaterials available, their properties, and the process to generate bioprinted constructs with application in medicine. Current challenges and the future path of bioprinting and bioinks will be addressed, with emphasis in mass production aspects and the regulatory framework bioink‐based products must comply to translate this technology from the bench to the clinic.