The least compressible material known, with a bulk modulus of 491 gigapascals (GPa) is aggregated diamond nanorods. They are what you get when you compress buckytubes, an allotrope of carbon, at 20 GPa, under a temperature of 2,500 Kelvin, using a 5,000 metric ton anvil press designed specifically for the purpose. The end result is a spaghetti of interconnected diamond nanotubes, with diameters between 5 and 20 nanometers and lengths of about a micrometer each.
A bulk modulus of these nanorods, 491 GPa, is about three times of that of iron, which is 160 GPa. Conventional diamond has a bulk modulus of 442 GPa. A bulk modulus of 491 GPa means that a pressure increase of 49.1 GPa would be necessary to compress the material by a factor of 10%, a 98.2 GPa pressure increase would be necessary to increase it by 20%, and so on. For comparison, the pressure at sea level (1 atmosphere) is equal to about 100 kPa (kilopascals), and every 32.8 feet (10 meters) of descent in the ocean increases pressure by another atmosphere. So the lowest point in the ocean, about 6.2 miles (10 km) down, experiences a pressure increase of 100 MPa over the surface, which would be enough to compress a solid sphere of aggregated diamond nanorods by a factor of .002%.
They get their strength from the famous sp2bond, the strongest bond in all of chemistry. This is a carbon-carbon bond, also found in graphite (along atom-thick 2D planes), in diamond (3D), and carbon nanotube fiber (which has been proposed as a building material for space elevators). The sp2 bond is not just the strongest known chemical bond, it is the strongest possible chemical bond, so these nanorods may not only be the least compressible material that scientists currently know, but the least compressible material, period. The only exception may be the exotic matter inside of super-dense stars, sometimes called neutronium.
Remarkably, these nanorods are even denser than pure diamond by a factor of 0.3%. Their appearance is dark with a slight rainbow-like scattering of light, similar to an oil slick on asphalt. Other substances less compressible than diamond, but more so than aggregated diamond nanorods, include type IIa diamond and ultrahard fullerite.