An effective representation of additive manufacturing (AM) data is important for ensuring the repeatability of AM processes and the reproducibility of AM parts. Recently, several standardised representations have been developed and used in the industry. While at the same time, a number of other representations have been presented within the academia. The coexistence of different representations generates a series of questions and discussions: What is a representation of AM data? Are the standardised representations comprehensive enough to ensure the repeatability and reproducibility? What challenges have been addressed so far in the presented representations? What are the strengths and weaknesses of each representation? What are the main issues in the field of AM data representation currently? What are the potential research directions of AM data representation in the future? To approach these questions, a review of the existing representations of AM data is presented in this paper. Firstly, an in-depth analysis of the existing representations is provided. Then, detailed comparisons among these representations are made, and a discussion about the main issues in AM data representation is carried out on the basis of the comparisons. Finally, some future research directions of AM data representation are suggested.