Progress in the electrospinning techniques has brought new methods for the production and construction of various nanofibrous assemblies. The parameters affecting electrospinning include electrical charges on the emerging jet, charge density and removal, as well as effects of external perturbations. The solvent and the method of fiber collection also affect the construction of the final nanofibrous architecture. Various techniques of yarn spinning using solid and liquid surfaces as well as surface-free collection are described and compared in this review. Recent advances allow production of 3D nanofibrous scaffolds with a desired microstructure. In the area of tissue regeneration and bioengineering, 3D scaffolds should bring nanofibrous technology closer to clinical applications. There is sufficient understanding of the electrospinning process and experimental results to suggest that precision electrospinning is a real possibility.