Experimental methods, apparatus, and practically useful theoretical analysis are provided for the coagulation-based spinning of effectively unlimited lengths of carbon nanotube fibers having exceptional toughness and reasonably high strength. This spinning process fundamentally depends on the mechanical properties of intermediate gel state fibers, which we find are surprising elastic up to about 20 % strain and sufficiently strong for diverse processing methods. More specifically, we show that assemblies of these gel fibers can be used as intermediates for making nanotube sheets, large diameter fibers, and conformal coatings. When suitably processed, these composites (comprising many parallel solution-spun nanotube fibers) have useful strength and extraordinary toughness.