Synthetic microfibers for non-woven textiles are predominantly made by spinning and drawing methods that involve extrusion through a nozzle to form the fiber.  Here, we report a new nanospinning method where fibers are formed by shear extension and anti-solvent based precipitation in bulk solution, which has advantages compared to all the existing methods of fiber formation.  Most significantly, instead of using nozzles, the method relies on combined capillary instabilities and shear extension to form the fibers.  This is especially desirable for the incorporation of various particle additives in composite fibers, which is problematic for traditional wet-spinning due to clogging of the nozzles.  Compared to electrospinning, the process is straightforward to scale up.   It is also applicable to a wide range of polymers, including responsive ones.  The fiber diameters are ~ 1-2 μm – up to ten times smaller than in wet-spinning.  We demonstrate fibers of various polymers and discuss their use in next-generation non-woven textiles.  Such small diameter fibers would find application in fine filtration, medical wound dressings, better barrier materials, and tissue scaffolds.