Nowadays, the implementation of digital thread for Additive Manufacturing (AM) and product data management system strongly depends on specified file formats and used interoperability standards in order to integrate geometric dimensioning and tolerancing (GD&T) information directly in the 3D CAD model. The consideration of geometric deviations and variations is a key issue for design and tolerancing, inspection and management of manufacturing part information in AM through product and manufacturing information (PMI). PMI has been used to describe GD&T and non-geometric data, such as surface texture, surface finishing requirements, material specifications, process data, and other annotations, based on ISO standards. Standards play an important role in enabling the interoperability and efficiency of AM systems through the development of AM standard formats. This paper reviews current challenges of geometric and tolerancing model and formats for AM processes, which largely impede the advancement of AM technologies. Two criteria to enhance AM geometric and tolerancing model and standards are presented in this paper: GD&T management and compliance with PMI. STL, AMF and STEP formats are discussed on their characteristics of product definition and manufacturing specification for AM. The review presented here highlights that STEP standard can be a good basis for future research work to integrate and standardise material information, geometric and tolerancing model, and process planning for AM. Finally, new specifications of STEP-AM format are proposed in this work.