Many types of tissue in the body, such as nerve, muscle, tendon, ligament, bone, and blood vessels, rely on a highly organized microstructure in order to impart their desired functionality. Cell and extracellular matrix (ECM) alignment in these tissues allows for increased mechanical strength and cell communication. In tissue engineering, aligned polymer nanofibers can be used to take on the role of natural ECM fibers in order to provide mechanical strength, sites for cell attachment, and modulation of cell behavior via morphological cues. A wide variety of physical and electrostatic techniques are available for assembly of aligned nanofiber structures, and many of these structures have been evaluated as tissue engineering scaffolds. It is widely understood that aligned microstructure induces an aligned morphology in most cell types, but aligned nanofibrous topography also influences other cell behaviors such as differentiation, gene expression, and ECM deposition. With a greater understanding of aligned nanofiber scaffold fabrication techniques, and cell interactions with these scaffolds, researchers may be able to overcome current challenges and develop better strategies for regenerating aligned tissues.