Electrospinning has emerged as a very promising technology enabling the production of synthetic polymeric, ultrafine fibres. These fibres have diameters in the submicron range, which results in a high specific surface area, and they are assembled as a non- woven mesh-like structure characterised by a high porosity and interconnectivity. Additionally, these nanofibre meshes can mimic physically the structure of the natural extracellular matrix of most connective tissues and, therefore, can be used as scaffolds for tissue engineering. However, the as-spun nanofibres meshes have two important drawbacks that may compromise a successful reconstruction or regeneration of thick tissues: the inherent planar structure, a pore size in the micron range and poor mechanical properties. In the present chapter, four alternative strategies are presented to overcome the identified limitations of its planar structure, allowing development of complex ordered fibrous structures that mimic the typical hierarchical organisation of tissues. The pore size of the electrospun nanofibre meshes obtained is typically too small to facilitate cell migration into the inner regions of the nanofibrous scaffold. This chapter addresses the issue of lack of cellular infiltration into an electrospun nanofibrous mesh, favouring different strategies to overcome those important structural issues. Current efforts to increase the strength of electrospun fibres have been mainly focused on the production of smaller diameter fibres, post-electrospinning treatments, incorporation of filler materials or in blending. Future work around electrospun meshes for biomedical applications should focus on the development of highly biofunctional nanofibres, with effective compositions for specific applications.