The small and large strain mechanical behavior of polymer nanofibers is strongly size and time-dependent. The instantaneous modulus, yield stress and ultimate tensile strength of electrospun polyacrylonitrile (PAN) nanofibers were found to increase for reduced fiber diameters due to enhanced molecular orientation. However, the ductility of PAN and polystyrene (PS) nanofibers at their glassy state was more than one order of magnitude larger than bulk PAN and PS. The large strain mechanical behavior of PS nanofibers was shown to be controlled by the interrelation between molecular size and fiber diameter. Furthermore, microscale tension experiments with poly(lactic-co-glycolic acid) (PLGA) nanofibers have shown that significant hardening facilitates the vastly increased ductility of submicron scale fibers, with the cross-sectional fiber geometry controlling the details of the evolution of the fiber stress vs. stretch ratio law. As a result, nanoscale polymer fibers possess vastly larger specific capacity for energy dissipation compared to their macroscale counterparts. This attribute is significantly enhanced with strain rate which results in monotonically increased yield strength but leaves the ultimate strain quite unaffected. This outstanding mechanical response was demonstrated for homogeneously deforming PAN nanofibers at strain rates as high a 200 s-1 and for PS nanofibers exhibiting stable necking at local plastic strain rates higher than 25,000 s-1. Furthermore, experiments with PAN nanofibers have shown decreasing creep compliance for reduced fiber diameters. To capture this effect, the small scale time-dependent response of PAN nanofibers was modeled with a linear viscoelasticity model containing diameter dependent time constants, which provided a good description for the creep and strain rate behavior. The size dependent, large deformation behavior was approximated via a modified rubber elasticity model which captured quite well the evolution of the mechanical response of PAN nanofibers.