With their impressive individual properties, carbon nanotubes should form high-performance fibers. We explored the roles of nanotube length and structure, fiber density, and nanotube orientation in achieving optimum mechanical properties. We found that carbon nanotube fiber, spun directly and continuously from gas phase as an aerogel, combines high strength and high stiffness (axial elastic modulus), with an energy to breakage (toughness) considerably greater than that of any commercial high-strength fiber. Different levels of carbon nanotube orientation, fiber density, and mechanical properties can be achieved by drawing the aerogel at various winding rates. The mechanical data obtained demonstrate the considerable potential of carbon nanotube assemblies in the quest for maximal mechanical performance. The statistical aspects of the mechanical data reveal the deleterious effect of defects and indicate strategies for future work.