The material with the greatesttensile strength is carbon nanotube fiber. It is also the stiffest known material, with a tremendously high elastic modulus, meaning it doesn't stretch easily. Carbon nanotubes can be visualized as graphene sheets curled into cylinders just a molecule wide.
These cylinders may have single walls (SWNTs or single-walled carbon nanotubes) or multiple walls (MWNTs or multi-walled carbon nanotubes). Multi-walled carbon nanotubes have been measured as the material with the most tensile strength of all, measuring in at 63 GPa (gigapascals) for atomic-scale testing, well below the theoretical maximum of 300 GPa. Scientists have not yet been able to produce this tensile strength in bulk materials, though work is ongoing and eventual success seems likely.
In contrast to carbon nanotubes, high-carbon steel has a tensile strength of about 1.2 GPa. Bulk carbon nanotube fiber has been created with a tensile strength of 1.6 GPa, which is the most tensile strength of any fiber, natural or artificial, by over an order of magnitude. Further improvements by another order of magnitude seem plausible over the next few decades. Carbon nanotube fiber is so strong that a 50,000 km-long (31,070 mile) cord of the fiber could be extended from the Earth's surface into geosynchronous orbit and it would not break. This concept is known as a space elevator.
In May 2007, researchers funded by the US Navy succeeded in making carbon nanotubes with a length exceeding 2 mm, the longest yet. The length-width ratio of these nanotubes is approximately 900,000 to 1. The Navy is understandably interested in fibers with the most tensile strength possible, as it uses ropes for numerous purposes such as mooring, fastening cargo, etc. Stronger fibers would allow for submersible ROVs (remotely operated vehicles) to weigh more, travel deeper, and be more reliably tied to their base stations, relevant in light of a $15 million Japanese ROV, among the most advanced in the world, which was recently lost over the course of a strong storm. Thus fibers with the most tensile strength would boost our ability to explore the ocean floors.
Similar benefits could propagate into all domains of engineering and design. Bridges could be made much stronger, if carbon nanotube fiber became more affordable. Currently it costs hundreds or thousands of dollars per gram, but the cost has been falling exponentially in recent years.