Sea urchins make homes for themselves by chewing through rocks, and the fact that their teeth manage stay sharp while doing this may show us humans how to make self-sharpening knives.
After literally decades of research, scientists have figured out how sea urchins can eat their way through rocks while keeping their teeth razor sharp. The secret is how the teeth are constructed: layers of calcite biocrystals held together with calcite nanocement are interspersed with softer layers of organic material, and when the teeth start to get dull on the surface, the top organic layer flakes off, exposing a brand new and freshly sharp layer of calcite. Chew, flake, repeat, and you've got infinitely sharp teeth.
Now that scientists know how the urchins do it, they say that it's at least theoretically possible to create a material with the same properties that could be made into knives and other tools that would sharpen themselves with use. Of course, we can't (yet) make knives that keep growing back like the urchin's teeth do, but at least you'd have something that stayed razor sharp until you wore it down to a nub.