Synthetic microfibers for non-woven textiles are predominantly made by methods that involve extrusion through a nozzle to form the fiber. A technology for wet-spinning of microfibers would greatly expand the range of microfiber feedstocks, and possible microfiber products. We will report a new nanospinning method where fibers are formed by shear extension and anti-solvent based precipitation in bulk solution. Instead of using nozzles, the method relies on combined capillary instabilities and shear extension to form the fibers. This is desirable for the incorporation of various particlulate 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 applicable to a wide range of polymers: we demonstrate fibers from recycled, renewable and biodegradable polymers. The fibers of diameter ~1-2 microns could find application in fine filtration, medical wound dressings, better barrier materials, and tissue scaffolds.