1973: Wolverine and young Professor X prevent Mystique’s assassination of Trask.
Magneto goes mad, moving a stadium over the White House with his powers.
Mystique then finds herself almost killing Trask again, but then decides not to, resulting in the new version of the same timeline.
Just before this, Magneto throws Wolverine into a lake with metal girders forced through his body.
His is then rescued by a young William Stryker who imprisons Wolverine with the purpose of casing his skeleton with adamantium, as part of the Weapon X project.1981: The events of X-Men Origins: Wolverine do not occur because Wolverine is already incarcerated by Stryker.
1983: The events of X-Men: Apocalypse occur.
Wolverine is freed from his imprisonment at the Weapon X facility by young Cyclops and Jean Grey, with his new adamantium skeleton and claws.
Sometime afterwards, a man in a suit arrives there and collects the blood of Wolverine, placing vials of it into a case marked “Essex Corp” - a fact that will be crucial for the events of Wolverine 3.
1991: The events of X-Men: Dark Phoenix occur. (X-Men: Dark Phoenix is released on November 2, 2018).
2000: It is unknown whether the events of X-Men occur or not.
2003: It is unknown whether the events of X2 occur or not.
2006: The events of X-Men: The Last Stand do not occur and Jean Grey doesn’t go crazy, so Logan doesn’t have to put her down.
2013: The events of The Wolverine do not occur as Jean Grey, Cyclops and Beast did not die.
2016: The events of Deadpool occur.
2023: Since the timeline has been altered, we see a glimpse of the new 2023 at the end of X-Men: Days of Future Past.
Things are as normal at Professor X’s school, with Wolverine a History teacher and Jean Grey and Beast very much alive.
Post-2023:
The Westchester Incident takes place, where an elderly Professor X has a seizure that injures 600 people and kills seven X-Men – as referenced in Logan.
Wolverine takes Professor X into hiding as Xavier's School for Gifted Youngsters is closed and the X-Men are disbanded.2029: The events of Logan take place.
No new mutants have been born for twenty years and Wolverine is living as a limo driver on the Mexican border with Professor X and Caliban.
Since the blood of Logan was picked up by Essex Corp in 1983, it's assumed that this produced
X-23, a female clone of Wolverine, known as Laura in the new film.
Scraping a living a a limo driver, Wolverine ends up on a road trip across the states being persuaded by dark forces who want to recapture X-23.