Biomimetic nanofibers have emerged as promising candidates for drug delivery and tissue engineering applications. In this paper, recent advances on the fabrication and application of biomimetic nanofibers as drug carriers and scaffolding materials are reviewed. First, we delineate the three popular nanofiber fabrication techniques including electrospinning, phase separation and molecular self-assembly, covering the principal materials used for different techniques and surface functionalization strategies for nanofibers. Furthermore, we focus our interest on the nanofiber-based delivery strategies and underlying kinetics for growth factors and other bioactive molecules, following which we summarize the recent advances in the development of these nanofibrous matrices for bone, vascular and neural tissue engineering applications. Finally, research challenges and future trends in the related areas are discussed.