Looking at the Earth's interior with neutrinos is a realistic possibility with current and future neutrino detectors, which is complementary to geophysics methods, but it is based purely on weak interactions. In this talk, I will discuss the two main approaches to perform Earth tomography with neutrinos: (i) neutrino absorption tomography, based on partial absorption of a neutrino flux as it propagates through the Earth (at energies about a few TeV) and (ii) neutrino oscillation tomography, based on coherent Earth matter effects on the neutrino oscillatory pattern (at energies below a few tens of GeV). I will first discuss (i) and present the first neutrino tomography of Earth using actual IceCube data. Then, I will discuss (ii) and, in particular, I will focus on supernova neutrinos with tens of MeV.