A spontaneous cheer went up when Indiana Jones was pulled out of the boot of a car in the Nevada desert. Nineteen long years have done nothing for his dress sense, and nor have they withered his appetite for trouble. This fantastic Steven Spielberg adventure is a marvellous return to form for Professor Henry Jones Jr. There are Mayan riddles to solve, KGB agents to biff, and one of the greatest - and longest - action chases through the Amazon jungle in the history of cinema.

Is this sane behaviour for a man in his mid-sixties? Of course not.

But we wouldn’t want it any other way. The hair under Harrison Ford’s famous fedora is now grey. The whip tucked into his trousers is a decidedly weird fashion accessory for pensioners in 1957. And the beam is slightly broader. But the curl of the lip is unmistakeable, and the humour is as pin-sharp as ever. It needs to be, because Indy is punched and battered from one end of this rollicking film to the other.

There are surprises galore. Elvis has been invented; aliens are all the rage. And Jones’s old flame Marion (played by Karen Allen) pitches up in the middle of darkest Peru to give the old bachelor a realistic girlfriend to shout at in the middle of a crisis. The professional adventurer also inherits a Brylcreemed tearaway called Mutt (Shia LaBeouf) as his side-kick, who roars into the picture on a classic Harley looking every inch like the young and moody Marlon Brando, cap akilter. This is Spielberg at his cheeky best.

The story of The Kingdom of the Crystal Skull is reassuringly chaotic. The Cold War is in full hue and cry, and Professor Jones' campus at Marshall University is a seething hotbed of communist paranoia. The Nazi treasure-hunters of yore have given way to the KGB with the same cartoon accents and “vays of making you talk”. The top Soviet fetishist, sorry scientist, Irina Spalko (aka Cate Blanchett) is scouring the globe for mythical relics called Crystal Skulls which collectively (there are 13 of them), have the psychic power to brainwash the world. This means trying to decipher John Hurt’s strange letters and Mayan clues which, for reasons totally beyond anyone’s ken, he has etched into the walls of a prison cell in Peru.

The film taps into all sorts of 1950s myths and horrors, which is why Indiana Jones makes his entrance in the desert. Soviet troops have kidnapped him to locate a skull hidden in a secret US military warehouse handily placed next to an atomic bomb-testing site. Indy manages to escape after initiating a duck-and-cover test by locking himself in a fridge. The fridge lands about eight miles away. “Do you know how many war medals this son of a bitch won?” barks a grizzled general when the FBI deign to question what Jones might be doing in a flying fridge in a military zone surrounded by the ashes of a couple of hundred dead Soviet soldiers.

After an intro like that, the rest of the film might have fizzled by comparison. Never, I repeat never, underestimate the extraordinary imagination of Steven Spielberg. The Kingdom of the Crystal Skull is an Olympic odyssey to discover El Dorado and the secrets of an ancient civilisation, and all the most beloved Indy challenges and horrors are conjured up like black magic. There are decrepit temples full of screaming skeletons and fiendish traps. There are rivers of giant army ants, and a trip over a triple-decker waterfall that brought tears of pure joy to the eyes. The only hollow moments are complex lumps of explication as Indy crunches through the potted history of Mayan civilisation, and the significance of ancient pictograms and maps, for the benefit of his unruly chums.

What makes these adventures such lucrative collectors' items are the legion of half-glimpsed nods to other films, and another era. When your fourth sequel takes 20 years to make, there is absolutely no way that you are going to return - a vital word in the film - without acknowledging in some form or other the kind of films and technology that have flowed under the bridge.

That said, Spielberg’s most remarkable achievement is to retain most of the old-fashioned virtues of the original franchise. He is light on the digital buttons, and the swashbuckling is truly great. Harrison Ford, amazingly enough, performs most of his utterly barmy stunts; the actor is in damn good shape for a 65-year-old professor. The Kingdom of the Crystal Skull is, quite simply, exquisite nonsense. Welcome back Indy. Lord knows we’ve missed you.

Editor's choice

• U2 at Nou Camp Stadium, Barcelona
• The 50 Best Movie Villains
• The 15 golden rules of theatre etiquette