On a January afternoon in 1981 a farmer in southern France heard a whistle in his garden and saw something settle on the terrace below him. Within a day gendarmes were on their knees collecting soil. Within two years a French government space agency had published the most detailed physical-trace report it would ever release. Forty-five years later, nobody agrees on what made the mark.

A 250 hectare wood on the edge of Cluj-Napoca is routinely called the most haunted forest on Earth. Behind the label sit four photographic negatives from August 1968, a circular clearing where trees will not grow, and decades of measurements that were never published. Here is what can actually be documented, and what cannot.

In late 1977, people on a small island at the mouth of the Amazon began arriving at the clinic with burns, puncture marks and stories of beams of light coming through their roofs at night. The Brazilian Air Force sent an officer to find out what was happening. Twenty years later, he broke his silence, and then he was dead.

On a September morning in 1994, the pupils of a small private school outside Harare came running in from morning break with the same impossible story. Thirty years, one Harvard psychiatrist and a shelf of crayon drawings later, nobody has explained what they saw.

On an autumn morning in 1966, a class of girls running laps on a Melbourne school oval stopped and pointed. Within minutes hundreds of students and teachers were watching a silver object sink behind the pines. By lunchtime they had been told to say nothing about it, and no official file has ever been produced.

On a clear March evening in 1997, thousands of people watched an enormous V of lights drift silently across 300 miles of Arizona sky. Two hours later a second set of lights hung over Phoenix and made the evening news. Nearly three decades on, the state's own governor is among those who say they still cannot explain what they saw.

Herodotus wrote that a Persian army marched into Egypt's Western Desert to burn an oracle and was buried alive by a sandstorm while eating lunch. Twenty-five centuries later, not one confirmed soldier of that army has ever been found. Two rival claims say they solved it, and most Egyptologists accept neither.

In 1912 a four-year-old walked away from a Louisiana swamp and vanished. Eight months later a boy was found on the road with a traveling handyman, and two mothers stood up to claim him. A court chose one of them. Ninety-two years later a DNA test proved the court had chosen wrong.

She was writing confessional singer-songwriter music in New York years before anyone called it that, and almost nobody heard it. In August 1974 she wrote a handful of calm farewell letters, packed her Volkswagen and drove out of Ann Arbor. Neither Connie Converse nor her car has ever been found.

On the morning he was due to fly to America, the lyricist of the Manic Street Preachers checked out of a London hotel and drove west, leaving his passport behind. Two weeks later his car turned up at a service station beside the Severn Bridge, battery flat, family photographs on the seat. Britain has been arguing about the rest for thirty-one years.

A crashed car on a dark New Hampshire highway. A bus driver who offered help and was turned away. Nineteen minutes later the police arrived and the driver was gone. Twenty-two years on, her phone and bank cards have never registered anywhere on earth.

She was nine years old, and at half past two in the morning she dressed, packed a bag and walked out into the rain. Drivers saw her on the highway; when one turned back she ran into the trees. A year and a half later her bag was dug up twenty-six miles away, wrapped in plastic and buried.