The invention relates to a porous self-standing homogeneous hydrogel comprising poly(vinyl alcohol) and carbon nanostructures, wherein: the carbon nanostructures are present in an amount from 7 to 85% by weight with respect to the sum of the weights of the poly(vinyl alcohol) and of the carbon nanostructures and the pores have an average particle size equal to or higher than 8 µm. It also relates to processes for the preparation of these hydrogels including phase inversion and cross-linking methods, and to their use in nerve regeneration.