The film is set in late 1999; there is an out of control nuclear satellite in orbit that is liable to reenter the atmosphere at any time, contaminating large areas of the earth. This has caused an increasing degree of disorder, with large numbers fleeing the likely impact sites. In the middle of all this, Claire Tourneur (Solveig Dommartin) has a couple of odd encounters; first with a couple of bank robbers (which ends up with her having a large pile of cash) and a hitchhiker who is being pursued by a number of groups. It turns out that the hitchiker's father absconded with the working prototype from a secret research project, and several government agencies, and some freelance bounty hunters are attempting to recover it.
The prototype is a device for recording and translating brain impulses - a camera for the blind - and her hitchiker is travelling the world, filming his widely-scattered family to show them to his blind mother. The chase continues round the world, the nuclear satellite is shot down, causing an EMP effect that wipes out all unshielded electronics worldwide, and the characters wind up in a hidden cave in the Australian Outback, where the recordings are played back.
To add to the (then) near-future look, at least one company, Sony, appears to have contributed prototypes of some of their planned new products for use in the film. The soundtrack is notable for Wenders asking various recording artists - U2, Talking Heads, REM etc. - for music to be used in the film; specifically for the music that they thought they would be making in 1999.