Drug delivery through tissue-engineered scaffolds provides a composite approach to address the regenerative limitations of simple material implantation, providing expanded avenues for therapeutic tissue-repair strategies in the clinic. Both nano- and microfibrous scaffolds generated by a variety of techniques have been investigated for their potential in drug-delivery applications. While nanofibers mimic the structure and organization of natural extracellular matrix, microfibers provide more sustained release of drugs, larger pores to facilitate cell infiltration, and improved mechanical support. Various methods exist to embed drugs within the fiber matrix to modulate the release kinetics specific to the tissue-engineering application. The current article reviews the established and emerging fabrication methods for drug-loaded fiber-based scaffolds and addresses how further combination into composite scaffolds can enhance drug delivery and tissue regeneration.