Additive manufacturing (AM) is considered the latest technology that creates breakthrough innovations and addresses complex medical problems. This is clearly demonstrated by the promising results obtained in regenerative medicine, diagnosis, implants, artificial tissues and organs. This paper provides a basic understanding of the fundamentals of 3D/4D printing along with bioprinting processes. We are briefly discussing about the main printing systems including stereolithography, inkjet 3D printing, extrusion, laser-assisted printing, selective laser melting and Poly-Jet printing. The basic requirements for the selection of successful inks based on polymers, polymer blends, and composites are described. Furthermore, the on-going transition from 3D to 4D printing is highlighted with emphasis on the newest applications in the medical area. Also, a glimpse into the future possibilities and benefits provided by machine learning in the additive manufacturing field is emphasized. Machine learning can improve printing efficiency by using generative design and testing in the pre-fabrication stage. Finally, important limitations and prospects are identified. Within the next few years, AM is set to become an important component in patient-specific medical technologies.