Attempts to design simultaneous interpreting equipment started in the 1920s with Edward Filene and Alan Gordon Finlay. The system was called “the Filene-Finlay simultaneous translator” and was used to read texts that had already been translated before the event.
No one thought at that time that “live” simultaneous interpretation was possible.
During the Nuremberg Trials after WWII we see simultaneous interpreting equipment that is more similar to what we have today.
A lot of credit in perfecting the equipment goes to the United Nations, where simultaneous interpretation was introduced (with some resistance at first) after World War II.