The Landau-Lifshitz-Gilbert equation (LLG) is a continuum model describing the dynamics for the spin in ferromagnetic materials. In the first part of this talk we describe the properties and dynamical behaviour of the self-similar solutions of this model in one dimension. Time permitting, and motivated by the properties of these solutions, we consider the Cauchy problem for the LLG-equation and provide a global well-posedness result provided that the BMO norm of the initial data is small.