The phenomenal advancement in regenerative medicines has led to the development of bioinspired materials to fabricate a biomimetic artificial extracellular matrix (ECM) to support cellular survival, proliferation, and differentiation. Researchers have diligently developed protein polymers consisting of functional sequences of amino acids evolved in nature. Nowadays, certain repetitive bioinspired polymers are treated as an alternative to synthetic polymers due to their unique properties like biodegradability, easy scale-up, biocompatibility, and non-covalent molecular associations which imparts tunable supramolecular architecture to these materials. In this direction, elastin has been identified as a potential scaffold that renders extensibility and elasticity to the tissues. Elastin-like polypeptides (ELPs) are artificial repetitive polymers that exhibit lower critical solution temperature (LCST) behavior in a particular environment than synthetic polymers and hence have gained extensive interest in the fabrication of stimuli-responsive biomaterials. This review discusses in detail the unique structural aspects of the elastin and its soluble precursor, tropoelastin. Furthermore, the versatility of elastin-like peptides is discussed through numerous examples that bolster the significance of elastin in the field of regenerative medicines such as wound care, cardiac tissue engineering, ocular disorders, bone tissue regeneration, etc. Finally, the review highlights the importance of exploring short elastin-mimetic peptides to recapitulate the structural and functional aspects of elastin for advanced healthcare applications.