The goal of drug delivery is to ensure that therapeutic molecules reach the intended target organ or tissue, such that the effectiveness of the drug is maximized. The efficiency of a drug delivery system greatly depends on the choice of drug carrier. Recently, there has been growing interest in using micro- and nanofibers for this purpose. The reasons for this growing interest include these materials' high surface area to volume ratios, ease of fabrication, high mechanical properties, and desirable drug release profile. Here, we review developments in using these materials made by the most prevalent methods of fiber fabrication: electrospinning, micro fluidics, wet spinning, rotary spinning, and self-assembly for drug delivery purposes. Additionally, we discuss the potential to use these fiber based systems in research and clinical applications.