Electrospinning technologies have been applied in the field of tissue engineering as materials, with nanoscale-structures and high porosity, can be easily prepared via this method to bio-mimic the natural extracellular matrix (ECM). Tissue engineering aims to fabricate functional biomaterials for the repairment and regeneration of defective tissue. In addition to the structural simulation for accelerating the repair process and achieving a high-quality regeneration, the combination of biomaterials and bioactive molecules is required for an ideal tissue-engineering scaffold. Due to the diversity in materials and method selection for electrospinning, a great flexibility in drug delivery systems can be achieved. Various drugs including antibiotic agents, vitamins, peptides, and proteins can be incorporated into electrospun scaffolds using different electrospinning techniques and drug-loading methods. This is a review of recent research on electrospun nanofibrous scaffolds for tissue-engineering applications, the development of preparation methods, and the delivery of various bioactive molecules. These studies are based on the fabrication of electrospun biomaterials for the repair of blood vessels, nerve tissues, cartilage, bone defects, and the treatment of aneurysms and skin wounds, as well as their applications related to oral mucosa and dental fields. In these studies, due to the optimal selection of drugs and loading methods based on electrospinning, in vitro and in vivo experiments demonstrated that these scaffolds exhibited desirable effects for the repair and treatment of damaged tissue and, thus, have excellent potential for clinical application.