In the video below, minutephysics explain how teleportation could be theoretically possible using quantum physics. Quantum teleportation uses quantum entanglement — a situation where one set of particles is dependent on the state of another. In principle, if scientists create specific sets of particles that are capable of being rearranged into whatever they wish to teleport, they can send partial information about one end of the entanglement — encoded as a quantum state — and thereby produce it in the other end. As an analogy: imagine taking a scan of what you want to transport, sending it to the other entangled particles, and rebuilding it from that.
While being able to transport anything large, like a cat — the example the video uses — is a long way off, scientists have managed to transport a single photon or electron about 100km. The difficulty lies in creating two entangled sets of particles and subsequently transporting one of them without it becoming disentangled.
This is linked to scientists achieving direct counterfactual quantum communication for the first time recently, which operates using the Zeno effect (freezing the situation by observing it) rather than entanglement. In the experiment, scientists successfully transported information using the phase of light.