In electrospinning, polymer nanofibers are formed by the creation and elongation of an electrified fluid jet. The path of the jet is from a fluid surface that is often, but not necessarily constrained by an orifice, through a straight segment of a tapering cone, then through a series of successively smaller electrically driven bending coils, with each bending coil having turns of increasing radius, and finally solidifying into a continuous thin fiber. Control of the process produces fibers with nanometer scale diameters, along with various cross-sectional shapes, beads, branches and buckling coils or zigzags. Additions to the fluid being spun, such as chemical reagents, other polymers, dispersed particles, proteins, and viable cells, resulted in the inclusion of the added material along the nanofibers. Post-treatments of nanofibers, by conglutination, by vapor coating, by chemical treatment of the surfaces, and by thermal processing, broaden the usefulness of nanofibers.