On-demand drug-delivery systems using nanofibers are extensively applicable for customized drug release based on target location and timing to achieve the desired therapeutic effects. A nanofiber formulation is typically created for a certain medication and changing the drug may have a significant impact on the release kinetics from the same delivery system. Nanofibers have several distinguishing features and properties, including the ease with which they may be manufactured, the variety of materials appropriate for processing into fibers, a large surface area, and a complex pore structure. Nanofibers with effective drug-loading capabilities, controllable release, and high stability have gained the interest of researchers owing to their potential applications in on-demand drug delivery systems. Based on their composition and drug-release characteristics, we review the numerous types of nanofibers from the most recent accessible studies. Nanofibers are classified based on their mechanism of drug release, as well as their structure and content. To achieve controlled drug release, a suitable polymer, large surface-to-volume ratio, and high porosity of the nanofiber mesh are necessary. The properties of nanofibers for modified drug release are categorized here as protracted, stimulus-activated, and biphasic. Swellable or degradable polymers are commonly utilized to alter drug release. In addition to the polymer used, the process and ambient conditions can have considerable impacts on the release characteristics of the nanofibers. The formulation of nanofibers is highly complicated and depends on many variables; nevertheless, numerous options are available to accomplish the desired nanofiber drug-release characteristics.