The paper gives a detailed review of the approaches adopted for embedding information into/onto additively manufactured parts. The primary purpose of this paper is to review all the techniques adopted for embedding information, highlight notable trends and improvements in these works, and provide design and manufacturing pipelines to realize most of these works. It classifies these approaches into four different categories and summarizes the works carried out in each field. It also compares all the results in textual and tabular forms and then gives a detailed conclusion of the best works in terms of application and effectiveness. The four categories discussed are 3D QR codes, 3D watermarking, steganography and nonclassified methods. Lastly, it discusses the future extensions and potential improvements in the field of embedding information, while exploring manufacturing technologies.