The use of biomaterials processed by the electrospinning technique has gained considerable interest for neural tissue engineering applications. The tissue engineering strategy is to facilitate the regrowth of nerves by combining an appropriate cell type with the electrospun scaffold. Electrospinning can generate fibrous meshes having fiber diameter dimensions at the nanoscale and these fibers can be nonwoven or oriented to facilitate neurite extension via contact guidance. This article reviews studies evaluating the effect of the scaffold's architectural features such as fiber diameter and orientation on neural cell function and neurite extension. Electrospun meshes made of natural polymers, proteins and compositions having electrical activity in order to enhance neural cell function are also discussed.