The Phoenix was a Human spaceship launched in 2063. Constructed from an old Titan V nuclear ICBM, the Phoenix was designed by Zefram Cochrane, and was the first vessel in Earth history to travel at warp speed (having reached a speed of warp 1.1). (TNG movie: First Contact, ST reference: Federation: The First 150 Years)
The first, and only, flight of the Phoenix took place on April 5, 2063. It was launched from Montana and was crewed by Cochrane, William T. Riker and Geordi La Forge. The ship's flight attracted the attention of a passing Vulcan ship, the T'Plana-Hath, leading to first contact between Humans and Vulcans. (TNG movie: First Contact)
As the singular vessel responsible for humanity's introduction to interstellar society the Phoenix is one of the most famous names in Earth and Federation history.
By the 24th century, the ship was part of the Smithsonian Institution collection and Jean-Luc Picard visited it there "hundreds of times" without physically touching the legendary vessel. (TNG movie: First Contact)
In 2373 the Borg sent a Borg sphere back through time to the day before the launch of the Phoenix planning to destroy it, thus preventing first contact and consequently preventing humanity from developing to be a source of great resistance in the future. Fortunately the USS Enterprise-E followed the sphere back through time and destroyed it before it completed its attack. The Enterprise crew then assisted in repairs to the damaged Phoenix to permit it to launch on time. (TNG movie: First Contact)
In 2293, in an alternate future created when Mia Colt was transported to the future by a keepsake, Colt and James T. Kirk shared a drink in an establishment called the Phoenix Tavern, which featured a full scale replica of the Phoenix’ cockpit and upper-section which hung along the ceiling. (EV comic: "Future Tense")
- Given the recent point of divergence (2254) it seems likely the Phoenix Tavern would exist in the main timeline as well.
In 2365 Kori, a child who lived in The Armada, owned a remote control model of the Phoenix. However, out of boredom, he fitted his model with explosives so that it exploded in flight. (TNG - The Space Between comic: "Space Seeds")