Textile production is a major component of the global industry, with sales of over USD 450 billion and estimations of an 84% increase in their demand in the next 20 years. In recent decades, protective and smart textiles have played important roles in the social economy and attracted widespread popularity thanks to their wide spectrum of applications with properties, such as antimicrobial, water-repellent, UV, chemical, and thermal protection. Towards the sustainable manufacturing of smart textiles, biodegradable, recycled, and bio-based plastics are used as alternative raw materials for fabric and yarn production using a wide variety of techniques. While conventional techniques present several drawbacks, nanofibers produced through electrospinning have superior structural properties. Electrospinning is an innovative method for fiber production based on the use of electrostatic force to create charged threads of polymer solutions. Electrospinning shows great potential since it provides control of the size, porosity, and mechanical resistance of the fibers. This review summarizes the advances in the rapidly evolving field of the production of nanofibers for application in smart and protective textiles using electrospinning and environmentally friendly polymers as raw materials, and provides research directions for optimized smart fibers in the future.