Despite being known for decades (since 1934), electrospinning has emerged recently as a very widespread technology to produce synthetic nanofibrous structures. These structures have morphologies and fiber diameters in a range comparable with those found in the extracellular matrix of human tissues. Therefore, nanofibrous scaffolds are intended to provide improved environments for cell attachment, migration, proliferation and differentiation when compared with traditional scaffolds. In addition, the process versatility and the highly specific surface area of nanofiber meshes may facilitate their use as local drug-release systems. Common electrospun nanofiber meshes are characterized by a random orientation. However, in some special cases, aligned distributions of the fibers can be obtained, with an interconnected microporous structure. The characteristic pore sizes and the inherent planar structure of the meshes can be detrimental for the desired cell infiltration into the inner regions, and eventually compromise tissue regeneration. Several strategies can be followed to overcome these limitations, and are discussed in detail here.