The feelgood fantasy of films that let us leap back in time

"This time-travel crap fries your brain like an egg." So says Jeff Daniels' mid-ranking criminal in Rian Johnson's new sci-fi film Looper. It's an apt statement for a sub-genre that continues to fascinate and frustrate filmmakers in equal measure. Because let's face it: time-travel movies, even the good ones, don't quite work. The logic will tie you up in a Möbius strip of knots until you drive yourself to distraction thinking about how altering events in the past will change the future.

Just a brief internet search will unveil dozens of sites devoted to deconstructing the temporal anomalies in even the most highly-regarded time-travel classics. How, for example, can the McFly siblings in the family photograph taken back in time in Back to the Future increasingly dissolve? Absurdly, the film theorises that this is simply because their parents' first encounter has been interrupted. But even if their births are jeopardised, how would this corrupt an already existing photo? Put it down to the grey area that is time-travel.

"It's a live-wire, a third rail in science fiction," says Johnson. "It's a tough, tough thing to deal with, logically speaking." Set in the near-future, his film posits a world where mob targets are sent back in time and killed by assassins known as "loopers", living 30 years earlier – to an era where time-travel has yet to be invented. Starring Joseph Gordon-Levitt as one of these loopers, the games begin when his future-self (played by Bruce Willis) is sent back as his next target.

If the casting of Willis is a direct nod to his role as a time-travelling convict in Terry Gilliam's Twelve Monkeys, Johnson seems not alone in his love of the genre. Already, we've had Men In Black 3 this year, taking Will Smith's Agent J back to 1969 to stop the murder of his partner. Meanwhile our own Richard Curtis has just shot About Time, a comedy he says is "about love, time-travel and the meaning of life" in which Domhnall Gleeson travels to the past to find himself a girlfriend (Rachel McAdams). "When you start thinking about time-travel it's a gripping subject, but I wanted to do a very small version of it," says Curtis. "So he can't travel places he hasn't been. He's always travelling within his own life."

At the other end of the scale is Colin Trevorrow's charming Sundance hit Safety Not Guaranteed. In it, a reporter and two interns go in search of the person behind an intriguingly written classified ad that reads: "Wanted: someone to go back in time with me. This is not a joke. You'll get paid after we get back. Must bring your own weapons. I have only done this once before. Safety not guaranteed."

That the advert is actually real, placed in the September 1997 issue of US survivalist magazine Backwards Home, makes the premise all the more delicious. Disappointingly, the explanation is rather more prosaic; author John Silveira, a senior editor at the magazine, placed it as a spoof page-filler. Nevertheless, it became an internet sensation. "John has boxes full of very sincere letters," reports Trevorrow, "from people like prisoners, who really want a time machine and were thinking it's real."

Therein lies the reason time-travel movies remain so popular. It's not just about travelling back to meet Napoleon or see the dinosaurs. There are "emotional needs", according to Trevorrow, that time-travel satisfies: the very thought that we can travel to bygone days, re-correcting costly mistakes and adjusting our destinies. However skewed the logic, it's going back to the past – and not the future – that keeps us hooked.

'Looper' opens on 28 September. 'About Time' and 'Safety Not Guaranteed' will open in 2013

Click here or on "View Images" to see the five best time-travel movies

*This article will appear in tomorrow's print edition of The Independent's Radar magazine