Because of their weak interactions, neutrinos can traverse matter like no other known particle. These elusive messengers can therefore be turned into a new probe to investigate the structure and composition of the deep Earth.
In this seminar, I will present the different methodological approaches to neutrino tomography, focusing on recent efforts exploiting either the oscillation or the absorption of atmospheric neutrinos in the Earth. I will then describe how these methods can be used and combined to investigate open questions in deep-Earth science.
The advent of a new generation of large-scale atmospheric neutrino detectors such as KM3NeT and IceCube, and in the future HyperKamiokande and even DUNE,  might finally bring these ideas into a concrete possibility that can be investigated with real data. The seminar will conclude with a discussion of the expected performances of these detectors for neutrino tomography, while paving the way to a next-generation instrument fully optimised for Earth tomography.