During the past decades of applications of DFT for solids, emphasis has been mostly on predicting properties of given crystal structures. Recently, systematic methods are being developed at various places to go one step further: predicting the crystal structure itself, with no a priori information given [1-5]. In this seminar, preliminary results will be discussed on the application of structure prediction tools to a prototype problem in geophysics: what is the crystal structure of the Inner Core of the Earth -- a solid sphere (radius 1220 km) of a Fe90Ni10+impurities alloy subject to high pressure (350 GPa) and high temperature (6000 K)?