Tissue engineering involves the in vitro seeding of cells onto scaffolds which assume the role of supporting cell adhesion, migration, proliferation, and differentiation, and which define the three-dimensional shape of the tissue to be engineered. Among the various types of scaffold architectures available, scaffolds based on nanofibers mimicking to a certain extent the structure of the extracellular matrix offer great advantages. Electrospinning is the technique of choice for the preparation of such scaffolds. Investigations have revealed that the nanofibrous structure promotes cell adhesion, proliferation, and differentiation. Parameters relevant for these processes such as fiber diameters, surface topology, porosity, mechanical properties, and the fibrous architecture of the scaffold can be controlled by electrospinning in a broad range.