What Doesn't Exist

Dry Molecular Nanotechnology: Modern “wet” nanotechnology uses DNA, self-assembling protein molecules, and gengineered viruses. Nanoscale systems are products of top-down assembly using atomic force microscopes. “Dry” nanorobots working at the molecular level are still confined to the lab.
Force Fields: No fields exist that can stop solid objects or directed energy beams.
FTL, Time Travel, and Gravity Control: No faster-than-light (FTL) travel or communications system, or time-travel technology, has been developed, nor have any machines been built to neutralize or create gravity. Some researchers hope that the study of primordial black holes may lead to breakthroughs.
Reactionless Drives: None have been invented.
Room-Temperature Superconductors: These have been achieved (such as metallic hydrogen wires) but are too fragile, costly, or unstable for widespread use. Robust superconductors that require limited cooling do exist.