Teleportation

Teleportation is the transfer of matter between two points without occurring or passing in between those points. It is most similar to (but not the same as) the concept of science fiction's transporters in which the object or person is rendered into some (unspecified) form of energy, transmitted and re-assembled at a receiver.

Although some recent experiments have shown a similar effect with atoms, it should be noticed that every atom of the matter to be transported would require two additional and entangled atoms already in place, one at the transmitter and one at the receiver. The thing actually transmitted here is the quantum state of the atom, not the atom itself.

The amount of information required to specify the states of the number of atoms in a large object, a pinhead say, and to also specify their spatial relationships would be so large and require so much processing and transmission time as to render the process impossible with today's technology.

Of course there's also Heisenberg!

Parapsychology
As a parapsychological topic, teleportation is closely related to telekinesis and is just as unlikely.

Consciousness destruction
In the same principle as Theseus's or the paradoxes, one horrifying theory about this is consciousness destruction. Essentially, it states that when a conscious being teleports, they're killed, and an exact replica that thinks it's them replaces them. As this theory is completely unfalsifiable, it would just be safer to, if we ever invent teleportation, restrict it to cargo transport.