In this talk, we present two mathematical approaches to fuse satellite images taken from different sensors. In the addressed model, remote sensing data are given by a hyperspectral (HS) image and a multispectral (MS) image covering the same scene. The HS image has a low-spatial but a high-spectral resolution, whereas the MS image has a high-spatial but a low-spectral resolution. The objective of the fusion of these two images is to obtain an image having the spectral resolution of the HS image and the spatial resolution of the MS one. The first proposed mathematical approach considers the HS-MS fusion as a barycenter problem in the optimal transport sense : the fused image minimizes the sum of two weighted Wasserstein distances, one related to the HS image and the other to the MS image. Due to the high dimensionality of HS-MS data, classical optimal transport algorithms do not give rise to a tractable problem. A relatively fast method is obtained by regularizing the Wasserstein distance with the entropy of the transport coupling, so that the optimization problem boils down to minimize a Kullback-Leibler divergence, allowing to apply the Sinkhorn’s algorithm. The second mathematical approach generalizes to the hyperspectral case a method for pansharpening images fusion introduced by J. Duran, A. Buades, B. Coll and C. Sbert in 2014. We propose a new variational model for which the function to be minimized performs a non-local gradient regularization so as to constrain the geometry of the fused image to that of the multispectral one. A data attachment term constrains high frequencies to respect those of the multispectral image and of the hyperspectral one. Experiments will be reported, which tend to establish that these two proposed approaches compare favorably with the state of the art (joint work with Jamila Mifdal, Bartomeu Coll, Nicolas Courty and Joan Duran).