Tissue engineering and regenerative medicine (TERM) are attracting more and more attention for treating various diseases in modern medicine. Various biomaterials including hydrogels and scaffolds have been developed to prepare cells (particularly stem cells) and tissues under 3D conditions for TERM applications. Although these biomaterials are usually homogeneous in early studies, effort has been made recently to generate biomaterials with the spatiotemporal complexities present in the native milieu of the specific cells and tissues under investigation. In this communication, the microfluidic and coaxial electrospray approaches that we used for generating microscale biomaterials with the spatial complexity of both pre-hatching embryos and ovary in the female reproductive system were introduced. This is followed by an overview of our recent work on applying the resultant bioinspired biomaterials for cultivation of normal and cancer stem cells, regeneration of cardiac tissue, and culture of ovarian follicles. The cardiac regeneration studies show the importance of using different biomaterials to engineer stem cells at different stages (i.e., in vitro culture versus in vivo implantation) for tissue regeneration. All the studies demonstrate the merit of accounting for bioinspired complexities in engineering cells and tissues for TERM applications.