Invisible thread has been a magic mainstay since its discovery in the 1960s by a group of scientists doing research for NASA. It is a monofilament too thin to be seen by the human eye, but so strong that it can not be broken except for under the most extreme conditions. Invisible thread is, in fact, so thin that it can slip between the molecules of any other substance, cutting through steel as easily as through butter. (Note: a professional magician will never use invisible thread to cut butter, although mysteriously carving a Thanksgiving turkey is not out of the question.)
Invisible thread is sold on spools, and one spool will last a magician a lifetime. Because of its dangerous nature, invisible thread may be purchased only with a prescription.
There are, quite literally, billions of uses for invisible thread, documented in books such as the classic Why You Must Fear Invisible Thread. Perhaps the most famous use is the Levitating Assistant routine, in which the magician's assistant is put into a trance (necessary because working so near an invisible substance that can casually decapitate you makes most people very nervous) and floats into the air.
The method for this trick is almost laughably simple. The assistant lies down on a thick, iron-alloy table that has been painted black (so that the audience can't see it) and has a length of invisible thread wound around it and the rafters overhead. The thread is not tied to the table because it is nearly impossible to tie a knot in invisible thread without the use of a tunneling electron microscope.
With the assistant in place, the magician pulls very, very, very carefully on the spool of thread hidden in one hand, and the assistant is lifted into the air. Caution must be used, because a sharp tug could very easily turn this into an "assistant sawed in half" routine.
If the magician wants to pass a metal hoop around the assistant to "show that there are no wires," this is also easily done. The invisible thread will pass right through a metal hoop. The magician must be careful, however, not to pass the hoop over the floating assistant a second time, because if the invisible thread does not cut through the hoop in exactly the same position on the second pass, it will effectively cut a chunk out of the hoop. A new hoop is needed for each performance -- cuts at the subatomic level can not be repaired.
It is interesting to note that many companies will not provide health or accident insurance to magicians who use invisible thread.