The spreading dynamics of a droplet of pure liquid deposited on a rigid, nonsoluble substrate has been extensively investigated. In a purely hydrodynamic description, the dynamics of the contact line is determined by a balance between the energy associated with the capillary driving force and the energy dissipated by the viscous shear in the liquid. This balance is expressed by the Cox-Voinov law, which relates the spreading velocity to the contact angle. More recently, complex situations have been examined in which dissipation and/or the driving force may be strongly modified, leading to sometimes spectacular changes in wetting dynamics. We review recent examples of effects at the origin of deviations from the hydrodynamic model, which may involve physical or chemical modifications of the substrate or of the wetting liquid, occurring at scales ranging from the molecular to the mesoscopic.