Whether delicate embroidery or large-format tapestries, historical textiles are treasures from the past and, at the same time, a challenge for restoration and research. In the EU project »TEXTaiLES«, state-of-the-art technologies meet centuries-old cultural heritage: AI, robotics, 3D scans, and physical simulations enable digital recording, analysis, and virtual restoration. The results will benefit museums, conservators, and researchers across Europe in the form of a modular software toolkit. Our team provides the mathematics and physics behind the digital fabrics – for realistic motion analysis, precise drapery simulations, and sustainable conservation.