The Third World War lasted for ten years and 600 million people perished in the nuclear disaster. In 2053 an uneasy truce was signed. Around this time Zefram Cochrane began his construction of the first warp capable vessel of humanity, the Phoenix.
On April 5, 2063 at 11:15 Cochrane made humanity's first warp flight. His warp signatures were detected by a Vulcan survey ship which landed in the evening and made first contact with humanity. Development of warp technology was the Vulcan's prerequisite for "first contact" with a civilization, a practice that continues through to the present continuity of the United Federation of Planets.
Cochrane was played by Glenn Corbett in the episode "Metamorphosis" of Star Trek: The Original Series and by James Cromwell in the film Star Trek: First Contact.