Additive manufacturing (AM) is rapidly evolving from “rapid prototyping” to “industrial production”. AM enables the fabrication of bespoke components with complicated geometries in the high-performance areas of aerospace, defence and biomedicine. Providing AM parts with a tagging feature that allows them to be identified like a fingerprint can be crucial for logistics, certification and anti-counterfeiting purposes. Whereas the implementation of an overarching strategy for the complete traceability of AM components downstream from designer to end user is, by nature, a cross-disciplinary task that involves legal, digital and technological issues, materials engineers are on the front line of research to understand what kind of tag is preferred for each kind of object and how existing materials and 3D printing hardware should be synergistically modified to create such tag. This review provides a critical analysis of the main requirements and properties of tagging features for authentication and identification of AM parts, of the strategies that have been put in place so far, and of the future challenges that are emerging to make these systems efficient and suitable for digitalisation. It is envisaged that this literature survey will help scientists and developers answer the challenging question: “How can we embed a tagging feature in an AM part?”.