3D printing, also known as Additive manufacturing (AM), has emerged as a transformative technology with applications across various industries, including the medical sector. This review paper provides an overview of the current status of AM technology, its challenges, and its application in the medical industry. The paper covers the different types of AM technologies, such as fused deposition modeling, stereolithography, selective laser sintering, digital light processing, binder jetting, and electron beam melting, and their suitability for medical applications. The most commonly used biomedical materials in AM, such as plastic, metal, ceramic, composite, and bio-inks, are also viewed. The challenges of AM technology, such as material selection, accuracy, precision, regulatory compliance, cost and quality control, and standardization, are also discussed. The review also highlights the various applications of AM in the medical sector, including the production of patient-specific surgical guides, prosthetics, orthotics, and implants. Finally, the review highlights the Internet of Medical Things (IoMT) and artificial intelligence (AI) for regulatory frameworks and safety standards for 3D-printed biomedical devices. The review concludes that AM technology can transform the healthcare industry by enabling patients to access more personalized and reasonably priced treatment alternatives. Despite the challenges, integrating AI and IoMT with 3D printing technology is expected to play a vital role in the future of biomedical device applications, leading to further advancements and improvements in patient care. More research is needed to address the challenges and optimize its use for medical applications to utilize AM’s potential in the medical industry fully.