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Perhaps the most iconic of Trek gizmos that became reality was the device simply known as the "Communicator," a palm-sized walkie-talkie with a flip-out antenna that allowed crew members to communicate with each other while in the field, and allowed the Enterprise to geo-locate and communicate with the away team from orbit on any planet they happened to have beamed down on.
The real-life version of the "Communicator" became the mobile phone, which was invented by Dr. Martin Cooper of the Motorola corporation, and released in April 1973.
Cooper admitted to being inspired by the original Star Trek show as the driving force behind the device that now permeates virtually all of modern society. The original real-life "Communicator" was brick-sized, but Motorola eventually released the appropriately named StarTAC in 1996, which was a dead ringer for the Trek original.
Today, flip-style cell phones that look like the original Communicator have largely given way to more powerful touchscreen smartphones like the iPhone and the Samsung Galaxy, but without Star Trek, we probably wouldn't have seen either of them.
The true Communicator didn't use cell towers — it was able to broadcast over huge distances, and allowed crew members to communicate both planet-wide and to the ship in orbit without the use of any support infrastructure.
We haven't gotten there yet, and we sort of failed with mass adoption of global-capable Communicator tech with Iridium, but modern cell phones do permeate our lives, and we do have the ability now to locate each other with built-in GPS capabilities, which the Enterprise was able to do for its crew members.
In 2009, Google introduced the Latitude service, which allows anyone carrying a GPS-capable smartphone running Google Maps to be visually located by their friends, so we're getting closer to the "True" Trek Communicator.