Polymeric biomaterials exhibit excellent physicochemical characteristics as a scaffold for cell and tissue engineering applications. Chemical modification of the polymers has been the primary mode of functionalization to enhance biocompatibility and regulate cellular behaviors such as cell adhesion, proliferation, differentiation, and maturation. Due to the complexity of the in vivo cellular microenvironments, however, chemical functionalization alone is usually insufficient to develop functionally mature cells/tissues. Therefore, the multifunctional polymeric scaffolds that enable electrical, mechanical, and/or magnetic stimulation to the cells, have gained research interest in the past decade. Such multifunctional scaffolds are often combined with exogenous stimuli to further enhance the tissue and cell behaviors by dynamically controlling the microenvironments of the cells. Significantly improved cell proliferation and differentiation, as well as tissue functionalities, are frequently observed by applying extrinsic physical stimuli on functional polymeric scaffold systems. In this regard, the present paper discusses the current state-of-the-art functionalized polymeric scaffolds, with an emphasis on electrospun fibers, that modulate the physical cell niche to direct cellular behaviors and subsequent functional tissue development. We will also highlight the incorporation of the extrinsic stimuli to augment or activate the functionalized polymeric scaffold system to dynamically stimulate the cells.