The Lady and the Unicorn wall-hangings are one of the great masterpieces of the world. It was supposedly made at the end of the 15th century and was acquired by the Musée de Cluny in 1882. Since their discovery, the six tapestries have undergone more than a dozen restoration campaigns. Some of these have been quite invasive, leaving visible traces and contributing to considerable degradation. Furthermore, the incomplete documentation of these campaigns hinders their understanding. The study will be focused on the “Mon seul désir” and “le Toucher” tapestries. During two analysis campaigns, several contactless spectroscopic techniques were used to identify materials (dyes, mordants, fibres) in both medieval and restoration zones. This paper aims to show how the treatment of hyperspectral data in the short-wave infrared range can highlight restored areas that are otherwise invisible, as well as enabling the selection of more precise areas for punctual analysis. Other non-invasive and portable methods, such as optical microscopy, hyperspectral imagery in the visible range, X-Ray Fluorescence and fluorimetry, have been performed in those specific areas revealed by false colour imagery. The combination of these spectroscopic techniques allowed the identification of natural dyes in medieval parts, such as indigo and madder. It gave many clues to explain the advanced degradation of the restored areas carried out in 1889. For example, the chiné weaving technique, the use of waste wool, and different mordants (alum, iron, copper…) or dyes mixtures (weld + madder + cochineal) were found, explaining partly why the restorations are visible today as faded colours. The confrontation of hyperspectral images and punctual data with the recent restoration surveys provides a solid basis for a better understanding of the history of restoration techniques used on the Lady and the Unicorn tapestry, furthering our knowledge of those precious tapestries.