International audienceWe present an updated strong-lensing analysis of the massive cluster Abell 370 (A370), continuing the work first presented in L17. In this new analysis, we take advantage of the deeper imaging data from the Hubble Space Telescope Frontier Fields programme, as well as a large spectroscopic mosaic obtained with the Multi-Unit Spectroscopic Explorer (MUSE). Thanks to the extended coverage of this mosaic, we probe the full 3D distribution of galaxies in the field, giving us a unique picture of the extended structure of the cluster and its surroundings. Our final catalogue contains 584 redshifts, representing the largest spectroscopic catalogue of A370 to date. Constructing the model, we measure a total mass distribution th...