Nathanael Schaeffer Université de Grenoble I (Joseph Fourier) Numerical simulations have been successful to explain the magnetic field of the Earth for almost 20 years. However, the regime in which these simulations operate is in many respect very far from what is expected in the Earth's core, and especially the lack of turbulence and a weak magnetic field. Turbulence in the core is rather peculiar, as it is strongly influenced by both the rotation of the planet and the strong self-induced magnetic field. We will review some aspects and properties expected for the turbulence in the Earth's core. We also performed simulations attempting to push turbulence and field strength to the limits of nowadays computers. We report on these highly forced, low viscosity model, and show what we can learn about turbulence in the Earth's core.