Issues of fossil fuel and plastic pollution are shifting public demand toward biopolymer-based textiles. For instance, silk, which has been traditionally used during at least 5 milleniums in China, is re-emerging in research and industry with the development of high-tech spinning methods. Various arthropods, e.g. insects and arachnids, produce silky proteinic fiber of unique properties such as resistance, elasticity, stickiness and toughness, that show huge potential for biomaterial applications. Compared to synthetic analogs, silk presents advantages of low density, degradability and versatility. Electrospinning allows the creation of nonwoven mats whose pore size and structure show unprecedented characteristics at the nanometric scale, versus classical weaving methods or modern techniques such as melt blowing. Electrospinning has recently allowed to produce silk scaffolds, with applications in regenerative medicine, drug delivery, depollution and filtration. Here we review silk production by the spinning apparatus of the silkworm Bombyx mori and the spiders Aranea diadematus and Nephila Clavipes. We present the biotechnological procedures to get silk proteins, and the preparation of a spinning dope for electrospinning. We discuss silk’s mechanical properties in mats obtained from pure polymer dope and multi-composites. This review highlights the similarity between two very different yarn spinning techniques: biological and electrospinning processes.