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Entering the flashing, bleeping world of the Barbican Art Gallery's Game On show is like stepping into an arcade circa 1975. The faces of teenage boys, eerily lit from below, seem hypnotized by consoles decorated with intergalactic centipedes. On the screens, a bear fights with waltzing trees and chorus lines of space jellyfish advance, firing from the hip. Videogames have reached their fourth decade, and the Game On exhibition traces their development from the simple tennis contest Pong to cinematic role-playing games like Final Fantasy. But the show is not just a timeline of game genres and chip development (plus a chance to play Tomb Raider), it also tries to make you think.

"Game On" — which runs at London's Barbican Centre throughout the summer and in mid-September moves to Edinburgh, then on to continental Europe, the U.S. and Japan — is divided into sections: games families, making and marketing, games culture, sound, cinema, future technology. There are driving games, sports games, kids' games and "twitch" games requiring rapid movements. There's ephemera in the form of magazines and fliers. You can listen to retro soundtracks or play games that create their own unique music. Eleven artists have been commissioned to produce related works.

With such a wide brief, some areas, such as cinema, seem rather squeezed, but many go into fascinating depth. Making and marketing includes a storyboard for the gangland adventure Grand Theft Auto taken straight from from the studio wall, which leads to a consideration of story-telling. "Narrative in video games is very non-linear," says curator Conrad Bodman. "There are subplots that may not lead to anything, but you have to work them all out" to find out what you have to do to win. The labyrinthine plot and convincing design may create a world in which players like to linger, but "Winning is always the final conclusion."

The show follows the way action games developed from text games — which describe a scenario and invite you to type in actions for your character to perform — putting the same kind of story into a realistic environment. You may find yourself on Monkey Island and set out to explore it, solving puzzles and following clues. Action games have become ultrasophisticated, with realistic lighting and weather effects. Some take place in vast mazes where it's "70 hours before you come back to the same place," says Bodman, as he pilots a flying saucer along a network of tunnels.

If action isn't your bag, you can try a real-life simulation like SimCity. It's really "a management sim[ulation]," says Bodman. You are "town planner, chief executive, deity even," supplying roads, housing, electricity, employment. The exhibition's section on The Sims, the virtual dollhouse bought by more women than men, shows original designs for characters and decor, as well as artwork by painter Ocean Quigley, who has worked on the series.

One of the exhibition's objectives is to highlight the role of the artists behind the games. Commentators don't often talk about the aesthetics, says Bodman, preferring to concentrate on sales. Another aim is to raise questions about the morality of violence in games like Mortal Kombat, and the relationship between such content and real war. An art installation by Mark Dean uses footage shot from the cockpit of a World War II bomber. "It's asking you to think about what you're doing when playing games," says Bodman. "It's warning us to remember what we're seeing."

The link between games technology and other disciplines is also explored. A local architectural practice has used software from the shoot-'em-up Quake to let clients walk around virtual buildings and check out the view from the windows. An interface that creates ripples in an on-screen vertical water surface when you wave your hands could lead to a whole new way of controlling software without the need for a keyboard, mouse or joy pad. Game On has something for everyone, whether you're an obsessive gamer, a student of media studies, a mom, a dad or a kid.

• LUCY FISHER/London
• Britain's first video game exhibition traces the history, makes you think and lets you play