Electrospinning technique has been extensively acknowledged as an efficient and convenient approach for producing functional nanofibrous biomaterials. The performance of the electrospun nanofibers and their nanofibrous membrane can be improved by modifying/combining with active molecules in different ways. The topography and orientation of the fibrous assembly are effectively controlled by modifying the electrospinning setup. Despite the promising characteristics of nanofibers, insufficient mechanical properties, hydrophobic nature, ineffective pore-structure controllability, shrinkage, and distortion are identified as some limitations. Yet, recent studies have been devoted/combined with other approaches to overcome these disadvantages. This chapter summarizes the recent strategies employed to develop advanced electrospun nanofibrous membranes for biomedical and tissue-engineering applications.