Time travel might exist in some theories, but in practice, it's never happened - unless some savvy time traveller did not announce their presence but gleaned useful information, like the upcoming Lotto results, and went back, or forward, to take advantage of it (that's what I'd do).
But in movies, where anything can happen, playing with time happens quite a bit, to both comic and dramatic effect. Long Story Short is a recent Australian example with a none-too-subtle moral. Perennial procrasinator Patrick (Rafe Spall) is given a wedding gift - or is it a curse? - by a mysterious stranger he meets in a cemetery (she's played by Noni Hazlehurst, but this isn't Play School).
Every few minutes another year has passed and it's his wedding anniversary again. Things keep changing - and not for the better. And he's the only one who knows what's happening as he ages and finds his marriage is deteriorating and his daughter is growing older, among other things.
It's no real spoiler to say "seize the day" is a key message of the film, though how Patrick is supposed to do this when he keeps losing a year at a time is not really explained.
Another "message" movie about time is Groundhog Day. More comedic than the bittersweet Long Story Short, Groundhog Day is about a misanthropic, self-centred weatherman (Bill Murray) who must go through his own special purgatory, having to relive the same day over and over until he learns to be the best person he can be. There's no personified instigator here: it just happens.
At least Murray's character didn't lose any time, unlike Spall's, and was able to put the repeating cycle to good use (learning French and piano, for example).
In one of Woody's better latterday films, Midnight in Paris, Owen Wilson's disenchanted character learns a different lesson. Each night, he magically escapes from family and work pressures to Paris in the past, hanging out with the likes of Cole Porter and Ernest Hemingway. Eventually he has to decide whether to live (literally) in the past and risk it becoming stale or embrace the possibilities of the present.
Sometimes time travel is not so much about learning a lesson but a matter of survival. Marty McFly in Back to the Future goes from the 1980s to the 1950s and, referencing the grandfather paradox, has to get his parents to fall in love at high school, lest they not marry and produce him and thus he will disappear (but then, if he didn't exist, neither would the story in the first place - though the sequels play around with this notion and things get complicated).
Marty's challenge is made worse by an Oedipal nightmare: his mother-to-be is attracted to HIM (could Marty be his own father? Now there's a slightly icky point to ponder....)
In the Bill & Ted series of movies, it's not just the life of one person that needs saving, but the entire world. The dopey duo of the title - wannabe rockers - discover their music will be the basis of an idyllic society. But there are plenty of challenges to meet, such as not flunking high school history.
Using a time machine, the boys are able to enlist help from such notables as Socrates and Napoleon (a lot more work than simply reading a textbook, but probably a lot more fun).
Further challenges include dicing - well, Battleshipping and Twistering - with Death and being pursued by a time travelling robot.
Speaking of time travelling robots, remember The Terminator? Arnold Schwarzenegger played the relentless killing machine sent to off Sarah Connor before she gave birth to the guy who would grow up to lead the resistance against the machines of the future.
The Arniemator would become a good guy and the sequels would become more involved (and when sans Arnie, less enjoyable).
Looper has a vaguely similar premise, with crime syndicates hiring "loopers" to go back in time and kill designated victims - and, eventually, themselves. Buying Joseph Gordon-Levitt as the young Bruce Willis was just one of the challenges.
Time travel is an integral part of - spoiler alert, if necessary - the original Planet of the Apes series that began in 1968. The surviving astronaut from Earth discovers, of course, that he has travelled through time and the titular planet is his own, in the future, after humankind has nuked itself out of existence (the fact that the primates spoke English should have been a tip-off).
At the end of the first sequel, the Ape-Earth was blown up, but you can't keep a successful franchise down: an ape family travelled to present-day Earth (ie the 1970s) in the next film and the series eventually wound around to end more or less where it began, albeit on a more hopeful note.
All time travel movies raise questions but some seem to deliberately set out to mess with your mind.
Christopher Nolan's Memento played out backwards and Interstellar was even more complicated with its wormholes and tesseracts and event horizons and other stuff that made some of us feel we needed degrees in science and mathematics just to work out what was going on and where, when, and why.
Being made to think about a movie is one thing, having to go back to university to understand what's going on is quite another.
After that, I am not too sorry I haven't caught up with Nolan's Tenet yet. I will need to find a smarter friend to watch it with me - and Donnie Darko, too. All these time loops and crashing planes and weird bunny costumes, it's just too much to try to unravel by myself. Maybe these are meant to be date movies for nerds.