The space-time telegraph was a device given by the Doctor to the Brigadier, to be used to summon him to Earth in the case of an emergency.
The Brigadier used it to get the Fourth Doctor to assist in investigating destroyed oil rigs. (TV: Revenge of the Cybermen, Terror of the Zygons)
The Brigadier used it again to bring the Doctor back for a training exercise, resulting in an argument between the two men. (PROSE: Hello Goodbye)
In 1996, Coldicott, on behalf of the United Nations, used it to get the Eighth Doctor to investigate the Remote. (PROSE: Interference - Book One)
In 2001, the Brigadier used it to contact the Sixth Doctor for help in investigating the mysterious events in Turelhampton (PROSE: The Shadow in the Glass)
In the 21st century, the World Ecology Bureau asked UNIT to use the space-time telegraph to summon the Doctor to assist them investigating Alex Marlowe. (AUDIO: Hothouse)
After Elizabeth Klein met the Master during his plan to rule all dimensions, the Seventh Doctor gave her a space-time telegraph to call him if she ever needed him. (AUDIO: UNIT:Dominion)
The space-time telegraph eventually came to be stored in the UNIT Black Archive. When several Zygons infiltrated UNIT and Kate Lethbridge-Stewart activated the Black Archive's self destruct, the Eleventh Doctor, along with the Tenth and War Doctor, contacted her via the telegraph to try to stop her sacrificing London to save the world. Despite their warning, Kate felt she had no choice and ordered the telegraph shut down. (TV: The Day of the Doctor)