A potential solution for prosthetic heart valves is tissue-engineered heart valves. Tissue-engineered heart valves (TEHVs) are designed to replicate the complex properties found in natural tissues, such as stiffness, anisotropy, and composition and organization of cells and extracellular matrix (ECM). Electrospinning is regarded as a highly versatile and innovative approach for fabricating numerous fibrous designs. In this review, we discuss recent developments in electrospun heart valve scaffolds, including scaffold materials, cell types, and electrospinning setups used to prepare aligned nanofibers. Despite the fact that natural biomaterials provided excellent biocompatibility, nanofibers from synthetic materials provided the required mechanical compatibility. Accordingly, most studies highlighted the benefits of designing composite heart valves using biological and synthetic polymers. Various strategies, such as the application of motorized mandrel and micropatterned collector in electrospinning were effective in controlling nanofiber alignment. Studies also showed that aligned nanofiber’s mechanical strength and anisotropic structure promote cell proliferation, and differentiation, and promote attachment. Numerous studies have reported that multiple cell sources are suitable for producing heart valves. Successful results were obtained with human umbilical vein endothelial cells (HUVECs), since they provide a convenient cell source for cellularization of valve leaflets. A higher conductivity of scaffolds was achieved by using biomaterials that conduct electricity, such as polyaniline, polypyrrole, and carbon nanotubes, which resulted in better differentiation of precursor cells to cardiomyocytes and higher cell beating rates. In light of these attributes, nanofibrous scaffolds produced through electrospinning are expected to offer numerous advantages for tissue engineering and medical applications in the near future. However, multiple challenges were identified as cell infiltration and 2D nature of nanofiber mats necessitate further engineering approaches in electrospinning procedure leaflet production.