The Earth’s core is one of the frontiers in earth science. Metallic cores play a central role in the chemical and thermal evolution of the Earth and the other planets, as their segregation is an important source for energy input in young planets and only their presences provide the opportunity for magnetic field generation. The different accretion and segregation histories of the terrestrial planets have resulted in diverse cores that we only begin to understand in recent years in terms of chemical composition, equations of state, and mineralogy of both the liquid and solid phases of Fe-alloys. Advances both in experimental and computational studies in geochemistry and mineral sciences of iron and Fe-alloys over the past decade were able to provide first insights into the variability of core structures for the terrestrial planets. In addition to contributions from the mineral sciences and geochemistry we encourage contributions from the wider community, including geodynamics, seismology, and planetary science that will lay out open questions in core structures of the planets.