This paper provides the state-of-the-art discussion of major aspects of the composition and evolution of the Earth's core. A comparison of experimentally-derived density of Fe with seismological data shows that the outer liquid core has a homogeneous structure and a ~10% density deficit, whereas the solid inner core has a complex heterogeneous anisotropic structure and a ~5% density deficit. Recent estimations of the core-mantle boundary (CMB) and inner core boundary temperatures are equal to 3800-4200 K and 5200-5700 K, respectively. Si and O (up to 5-wt.%) are considered to be the most likely light element candidates in the liquid core. Cosmochemical estimates show that the core must contain about 2 wt.% S and new experimental data indicate that the inner core structure gives the best match to the properties of Fe carbides. Our best estimate of the Earth's core calls for 5-wt.% Si, 0.5-1.0 wt.% O, 1.8-1.9 wt.% S, and 2.0 wt.% C, with the Fe7C3 carbide being the dominant phase in the inner core. The study of short-lived isotope systems shows that the core could have formed early in the Earth's history within about 30-50 Myr after the formation of the Solar System, t0 = 4567.2 ± 0.5 Ma. Studies on the partitioning of siderophile elements between liquid iron and silicate melt suggest that the core material would be formed in a magma ocean at ~1000-1500 km depths and 3000-4000 K. The oxygen fugacity for the magma ocean is estimated to vary from 4-to 1-log units below the Iron-Wustite oxygen buffer. However, the data for Mo, W, and S suggest addition of a late veneer of 10-15% of oxidized chondritic material as a result of the Moon-forming giant impact. Thermal and energetics core models agree with the estimate of a mean CMB heat flow of 7-17 TW. The excess heat is transported out of the core via two large low shear velocity zones at the base of superplumes. These zones may not be stable in their positions over geologic time and could move according to cycles of mantle plume and plate tectonics. The CMB heat fluxes are controlled either by high heat production from the core or subduction of cold slabs, but in both cases are closely linked with surface geodynamic processes and plate tectonic motions. Considerable amounts of exchange may have occurred between the core and mantle early in the Earth's history even up to the formation of a basal magma ocean. However, the extent of material exchange across the CMB upon cooling of the mantle was no greater than 1-2% of the core's mass, which, however, was sufficient to supply thermochemical plumes with volatiles H, C, and S.