Current cutting-edge strategies in biomaterials science are focused on mimicking the design of natural systems which, over millions of years, have evolved to exhibit extraordinary properties. Based on this premise, one of the most challenging tasks is to imitate the natural extracellular matrix (ECM), due to its ubiquitous character and its crucial role in tissue integrity. The anisotropic fibrillar architecture of the ECM has been reported to have a significant influence on cell behaviour and function. A new paradigm that pivots around the idea of incorporating biomechanical and biomolecular cues into the design of biomaterials and systems for biomedical applications has emerged in recent years. Indeed, current trends in materials science address the development of innovative biomaterials that include the dynamics, biochemistry and structural features of the native ECM. In this context, one of the most actively studied biomaterials for tissue engineering and regenerative medicine applications are nanofiber-based scaffolds. Herein we provide a broad overview of the current status, challenges, manufacturing methods and applications of nanofibers based on elastin-based materials. Starting from an introduction to elastin as an inspiring fibrous protein, as well as to the natural and synthetic elastin-based biomaterials employed to meet the challenge of developing ECM-mimicking nanofibrous-based scaffolds, this review will follow with a description of the leading strategies currently employed in nanofibrous systems production, which in the case of elastin-based materials are mainly focused on supramolecular self-assembly mechanisms and the use of advanced manufacturing technologies. Thus, we will explore the tendency of elastin-based materials to form intrinsic fibers, and the self-assembly mechanisms involved. We will describe the function and self-assembly mechanisms of silk-like motifs, antimicrobial peptides and leucine zippers when incorporated into the backbone of the elastin-based biomaterial. Advanced polymer-processing technologies, such as electrospinning and additive manufacturing, as well as their specific features, will be presented and reviewed for the specific case of elastin-based nanofiber manufacture. Finally, we will present our perspectives and outlook on the current challenges facing the development of nanofibrous ECM-mimicking scaffolds based on elastin and elastin-like biomaterials, as well as future trends in nanofabrication and applications.