We introduce InfraStructs, material-based tags that embed information inside digitally fabricated objects for imaging in the Terahertz region. Terahertz imaging can safely penetrate many common materials, opening up new possibilities for encoding hidden information as part of the fabrication process. We outline the design, fabrication, imaging, and data processing steps to fabricate information inside physical objects. Prototype tag designs are presented for location encoding, pose estimation, object identification, data storage, and authentication. We provide detailed analysis of the constraints and performance considerations for designing InfraStruct tags. Future application scenarios range from production line inventory, to customized game accessories, to mobile robotics.