Stem cells are considered as an integral part of tissue engineering and regenerative medicine. Cellular functions of stem cells, which are responsible for tissue organization, can be controlled and regulated by providing an appropriate microenvironment, which mimics native stem cell niche. Nanotechnology is a powerful tool for engineering cellular microenvironment in the form of scaffolds. The scaffolds that have nanoscale features, for example, nanofiber, are considered as an effective substratum for tissue regenerative applications because they structurally mimic the native extracellular matrix (ECM). Electrospinning is a technique which produces polymer nanofiber scaffolds with controlled size and orientation of the fibrous structure. These polymer nanofibers can be used to control stem cell fate and function, in particular cell adhesion, proliferation and differentiation, during tissue engineering. In this article, we focus on recent developments and research trends in polymer nanofibrous scaffolds and their impact in controlling and regulating stem cell fate and function.