Suddenly you fall to the ground. You can see a gray matter eating the legs of your bed. You run out of your house in panic. The whole street is sinking. Then suddenly holes fall in your clothes ... Nanorobots are about the size of a virus and promise a lot: a revolution in the extraction of raw materials, industry and medicine, to name a few. What would happen if they run wild and decide to try a human breakfast, for example?
Reducing things has big advantages. You need much less energy and raw materials to achieve the same. For example, a good pocket japanese can do more than the colossal one ENIAC computer which took up a complete living room with 30 tons. The smallest conceivable scale at the moment is that of the individual atom. Nanotechnology is a technique that manipulates things to an atomic level. Nanotechnology thus promises enormous advantages, because everything around us can be manufactured by arranging atoms in a different way. No wonder governments around the world are pumping billions into nanotechnology research.
Nanobots (or nanorobots) are nano-scale controllable machines.
All parts, such as motors, batteries and gripper arms, are made up of groups of atoms. It takes a lot of fiddling to build or manipulate things on a nanoscale. For example, you need an electron microscope with a sharp tip to see and move individual atoms. That is why many researchers use ready-made components such as enzymes (natural nanobots, as it were), carbon nanotubes and the like. Many researchers see the most in surfaces with nano properties. This is indeed the easiest (surfaces with nanostructures can be etched or printed, as is now the case with chips) and also safe.
However, nanorobots are more interesting for many applications. For example, a swarm of nanorobots could save the lives of patients by chiseling away blood clots and arteriosclerosis or by killing cancer cells. You can also have nano miners search for gold atoms while you sleep. Because nanorobots are so difficult to build, it makes sense to have nanorobots build other nanorobots. After all, you only have to build one nanorobot, which then copies itself.
In the gray goo doomsday scenario, coined by nanoprophet Eric K. Drexler in his book Engines of Creation self-replicating nanorobots escape. By the way, Drexler now regrets that, he thinks that other nano-hazards are much more urgent. They can generate enough energy to track down the atoms they need and use them to build new nanorobots. Everything around them is a resource for making more copies of themselves. Everything in their reach - houses, trees, people, rocks, air - turns into a wiggling mass of nanobots. There is no saving anymore. Even dropping an atomic bomb does not help: the pressure wave spreads the nanobots even further. In a period of a few weeks or months, the entire planet is covered with nanobots that gnaw the Earth and its inhabitants to the bone (and beyond). Astronauts aboard the ISS watch the entire Earth turn into a black lump.
There is of course a lot to criticize in this doomsday scenario. For example, energy at the nanoscale is scarce in many places. Nuclear energy is excluded, unless the nanobots construct a large nuclear power plant using chemical energy, for example. Nuclear fusion would also be possible in theory. Chemical energy is very scarce. For a nanobot to copy itself using chemical energy, it requires a multiple of the amount of atoms as fuel. Another fundamental problem is how the nanorobots can get rid of the waste heat. Rearranging atoms requires the necessary energy. So nanobots cannot grow too fast without getting themselves into trouble. Slow-growing nanobots can use sunlight as an energy source. There are currently solar panels that are more efficient than plants. Slowly replicating nanobots also have unpleasant consequences: because they are as small as bacteria, they are hardly to be found and are therefore ineradicable.
From a technical point of view, gray goo is conceivable in the medium to long term. In fact, our Earth is already saturated with biological replicators that can convert almost anything into themselves: bacteria.
On the other hand, someone will have to be stupid (and technically brilliant) enough to build a completely independent nanorobot that can replicate itself. Researchers expect this with strict regulations is preventable and design production processes in such a way that there is no need for separate reproducing robots on a nanoscale. For your reassurance, a universal nanobot that can live on many materials is likely to be extremely difficult, if not impossible, to build.