Digital twinning for Additive Manufacturing is challenging even though the starting point is an accurate nominal digital shape model of what is to be produced. Before the instructions controlling the additive machine are computed, the shape information goes through many tweaking steps as well as adaptations to the actual additive process, the feedstock and the manufacturing parameters used. Consequently, the outer shape produced is in general not an accurate copy of the nominal geometry that was the start point. To further complicate the situation, the actual additive manufacturing process and how it performed, as well as how the object is heated and cooled during and after manufacturing has a strong influence on the material properties of the object being produced (anisotropies, porosity, crystal structure). Thermal stress can result in shape deformations or cracks in the material. Thus, monitoring during the manufacturing process is important to create a high-quality digital twin of the process. In general, such monitoring by, e.g., image, thermal or eddy current sensors creates huge amounts of data that has to be analysed and interpreted to ensure that the object produced is qualified for the intended use, and to decide if it adheres to possible premanufacturing simulation of the AM process. The aim of the talk is to discuss the general challenges of digital twinning for Additive Manufacturing.