Star Trek: 10 Things You Need To Know About Transporters
4. Transwarp Beaming
Transwarp Beaming was demonstrated in the Kelvin-timeline films with a mixed reaction. In the film, it is Montgomery Scott who perfected the theory, though in the time that Spock-Prime travels back to, Scotty has yet to master it - much to the chagrin of Admiral Archer and his prize beagle. Spock shows him the theory required. However, this has a knock-on effect.
In Star Trek Into Darkness, rogue-Section 31 agent John Harrison/definitely not Khan uses it to escape Earth and travel all the way to Quo'nos. Though the film depicts this as a single beam, the novelization states that the device used didn't have enough power, requiring Khan to beam to a ship, then use the ship to beam to the Klingon homeworld.
Though this miracle device would seem to make Starfleet obsolete, it had actually been suggested by Gene Roddenberry in the initial development of Star Trek: The Next Generation. He put it forward as another cost-saving method, removing the need for a starship at all. Thankfully, writer David Gerrold shot that idea down straight away. The Enterprise is the hero, he said, delaying this technology for a further twenty years.