Tissue engineering has emerged as a biological alternative aimed at sustaining, rehabilitating, or enhancing the functionality of tissues that have experienced partial or complete loss of their operational capabilities. The distinctive characteristics of electrospun nanofibrous structures, such as their elevated surface-area-to-volume ratio, specific pore sizes, and fine fiber diameters, make them suitable as effective scaffolds in tissue engineering, capable of mimicking the functions of the targeted tissue. However, electrospun nanofibers, whether derived from natural or synthetic polymers or their combinations, often fall short of replicating the multifunctional attributes of the extracellular matrix (ECM). To address this, nanomaterials (NMs) are integrated into the electrospun polymeric matrix through various functionalization techniques to enhance their multifunctional properties. Incorporation of NMs into electrospun nanofibrous scaffolds imparts unique features, including a high surface area, superior mechanical properties, compositional variety, structural adaptability, exceptional porosity, and enhanced capabilities for promoting cell migration and proliferation. This review provides a comprehensive overview of the various types of NMs, the methodologies used for their integration into electrospun nanofibrous scaffolds, and the recent advancements in NM-functionalized electrospun nanofibrous scaffolds aimed at regenerating bone, cardiac, cartilage, nerve, and vascular tissues. Moreover, the main challenges, limitations, and prospects in electrospun nanofibrous scaffolds are elaborated.