Ab initio electronic structure calculations, based upon density functional theory within the generalised gradient approximation using ultrasoft non-norm-conserving Vanderbilt pseudopotentials, have been used to predict the structure and properties of crystalline and liquid iron and solid FeSi at conditions found in the Earth's core. The quality of the pseudopotentials used was assessed by calculating well documented properties of the solid phase: we have accurately modelled the equation of state of bcc and hcp Fe and FeSi, the bcc→hcp phase transition, the magnetic moment of bcc Fe, the elastic constants of bcc Fe, the bcc→bct distortive phase transition and the phonon frequencies for fcc Fe; the results show good agreement with both theory and experiment. Simulations were also performed on liquid iron and we present the first abinitio quantum molecular dynamics calculations on the structure and transport properties of liquid iron under core conditions. Our calculations show that the structure of liquid iron at the conditions to be found in the outer core is highly compressed with a first-neighbour coordination number inferred from the radial distribution function of ca. 12. We have also predicted a diffusion coefficient of 0.5×10^-4 cm² s^-1 indicative of a core viscosity of ca. 0.026 Pa s, in line with current estimates.