The impact of the inner structure and thermal history of planets on their observable features, such as luminosity or magnetic field, crucially depends on the poorly known heat and charge transport properties of their internal layers. The thermal and electric conductivities of different phases of water (liquid, solid, and super-ionic) occurring in the interior of ice giant planets, such as Uranus or Neptune, are evaluated from equilibrium ab initio molecular dynamics, leveraging recent progresses in the theory and data analysis of transport in extended systems. The implications of our findings on the evolution models of the ice giants are briefly discussed.