Extracellular matrix fibers (ECM) such as collagen, elastin, and keratin provide biological and physical support for cell attachment, proliferation, migration, differentiation and ultimately cell fate. Therefore, ECM fibers are an important component in tissue and organ development and regeneration. Meanwhile, polymer nanofibers could play the same critical role in tissue regeneration process. Fibrous structures can be fabricated from a variety of materials and methods with diameters ranging throughout the size scale where cells can sense individual fibers (several nanometers to several microns). Polymer nanofiber scaffolds can be designed in a way that predictably modulates a variety of important cell behaviors towards a desired overall function. The nanofibrous topography itself, independent of the fiber material, has demonstrated the potential to modulate cell behaviors desirable in tissue engineering such as: unidirectional alignment; increased viability, attachment, and ECM production; guided migration; and controlled differentiation. The versatility of polymer nanofibers for functionalization with biomolecules opens the door to vast opportunities for the design of tissue engineering scaffolds with even greater control over cell incorporation and function. Despite the promise of polymer nanofibers as tissue engineering scaffolds there have been few clinically relevant successes because no single fabrication technique currently combines control over structural arrangement, material composition, and biofunctionalization, while maintaining reasonable cost and yield. Promising strategies are currently being investigated to allow for the fabrication of optimal polymer nanofiber tissue engineering scaffolds with the goal of treating damaged and degenerated tissues in a clinical setting.