Accretion from primordial material and its subsequent differentiation into a planet with core and mantle are fundamental problems in terrestrial and solar system. Many of the questions about the processes, although well developed as model scenarios over the last few decades, are still open and much debated. In the early Earth, during its formation and differentiation into rocky mantle and iron-rich core, it is likely that silicate melts played an important part in shaping the Earth's main reservoirs as we know them today. Here, we review several recent results in a deep magma ocean scenario that give tight constraints on the early evolution of our planet. These results include the behaviour of some siderophile elements (Ni and Fe), lithophile elements (Nb and Ta) and one volatile element (Helium) during Earth's core formation. We will also discuss the melting and crystallization of an early magma ocean, and the implications on the general feature of core-mantle separation and the depth of the magma ocean. The incorporation of Fe2 + and Fe3 + in bridgmanite during magma ocean crystallization is also discussed. All the examples presented here highlight the importance of the prevailing conditions during the earliest time of Earth's history in determining the composition and dynamic history of our planet.