This review describes state-of-the-art scientific and technological developments of electrospun nanofibers and their use in self-cleaning membranes, responsive smart materials, and other related applications. Superhydrophobic self-cleaning, also called the lotus effect, utilizes the right combinations of surface chemistry and topology to form a very high contact angle on a surface and drive water droplets away from it. The high-contact-angle water droplets easily roll off the surface, carrying with them dirt, particles, and other contaminants by way of gravity. A brief introduction to the theory of superhydrophobic self-cleaning and the basic principles of the electrospinning process is presented. Also discussed is electrospinning for the purpose of creating superhydrophobic self-cleaning surfaces under a wide variety of parameters that allow effective control of roughness of the porous structure with hydrophobic entities. The main principle of electrospinning at the nanoscale and existing difficulties in synthesis of one-dimensional materials by electrospinning are also covered thoroughly. The results of different electrospun nanofibers are compared to each other in terms of their superhydrophobic properties and their scientific and technological applications.