Formation of the Earth and the other terrestrial planets of our Solar System (Mercury, Venus and Mars) commenced 4.568 billion years ago and occurred on a time scale of about 100 million years. These planets grew by the process of accretion, which involved numerous collisions with smaller (Moon- to Mars-size) bodies. Impacts with such bodies released sufficient energy to cause large-scale melting and the formation of deep “magma oceans”. Such magma oceans enabled liquid metal to separate from liquid silicate, sink and accumulate to form the metallic cores of the planets. Thus core formation in terrestrial planets was a multistage process, intimately related to the major impacts during accretion, that determined the chemistry of planetary mantles. However, until now, accretion, as modelled by astrophysicists, and core formation, as modelled by geochemists, have been treated as completely independent processes. The fundamental and crucial aim of this ambitious interdisciplinary proposal is to integrate astrophysical models of planetary accretion with geochemical models of planetary differentiation together with cosmochemical constraints obtained from meteorites. The research will involve integrating new models of planetary accretion with core formation models based on the partitioning of a large number of elements between liquid metal and liquid silicate that we will determine experimentally at pressures up to about 100 gigapascals (equivalent to 2400 km deep in the Earth). By comparing our results with the known physical and chemical characteristics of the terrestrial planets, we will obtain a comprehensive understanding of how these planets formed, grew and evolved, both physically and chemically, with time. The integration of chemistry and planetary differentiation with accretion models is a new ground-breaking concept that will lead, through synergies and feedback, to major new advances in the Earth and planetary sciences.