Kryptos is an encrypted sculpture installed at CIA headquarters in Langley, Virginia. It's a set of huge copper plates with enciphered text carved into them—for example, one segment reads TWTQSJQSSEKZZWATJKLUDIAWINFBNYP (though it looks a lot nicer in context).
Although the sculpture was installed in 1990, it took until 1999 for someone to actually decrypt part of the message: of the four segments of text, three were decrypted (complete with intentional spelling errors introduced by the sculptor, Jim Sanborn). The fourth segment remains encrypted, though there is an impressive online effort to decrypt it. Sanborn is reportedly so frustrated that the remaining bit has not been broken that he started giving out hints in 2010—still no breakthrough. He has also confirmed that in the event that he dies before the decryption occurs, the solution can still be confirmed. Jeepers.
The sculpture is puzzling for many reasons. First, you have the fact that encrypted text is sitting in a CIA courtyard, and part of that text is unknown—despite being surrounded by some of the world's best codebreakers. Second, the text that has been decrypted is totally bonkers, and seems to point to other puzzles and even an ancient crypt. Here are the segments that have been decrypted (note that misspellings and odd punctuation are intentional):
Solution 1 BETWEEN SUBTLE SHADING AND THE ABSENCE OF LIGHT LIES THE NUANCE OF IQLUSION Solution 2 IT WAS TOTALLY INVISIBLE HOWS THAT POSSIBLE ? THEY USED THE EARTHS MAGNETIC FIELD X THE INFORMATION WAS GATHERED AND TRANSMITTED UNDERGRUUND TO AN UNKNOWN LOCATION X DOES LANGLEY KNOW ABOUT THIS ? THEY SHOULD ITS BURIED OUT THERE SOMEWHERE X WHO KNOWS THE EXACT LOCATION ? ONLY WW THIS WAS HIS LAST MESSAGE X THIRTY EIGHT DEGREES FIFTY SEVEN MINUTES SIX POINT FIVE SECONDS NORTH SEVENTY SEVEN DEGREES EIGHT MINUTES FORTY FOUR SECONDS WEST X LAYER TWO Solution 3 SLOWLY DESPARATLY SLOWLY THE REMAINS OF PASSAGE DEBRIS THAT ENCUMBERED THE LOWER PART OF THE DOORWAY WAS REMOVED WITH TREMBLING HANDS I MADE A TINY BREACH IN THE UPPER LEFT HAND CORNER AND THEN WIDENING THE HOLE A LITTLE I INSERTED THE CANDLE AND PEERED IN THE HOT AIR ESCAPING FROM THE CHAMBER CAUSED THE FLAME TO FLICKER BUT PRESENTLY DETAILS OF THE ROOM WITHIN EMERGED FROM THE MIST X CAN YOU SEE ANYTHING Q ?
That last bit is a reference to Howard Carter's opening of the tomb of King Tut, so it's not entirely the ravings of a mad artist.
Kryptos shows up occasionally in pop culture—including on an episode of the Showtime series Homeland. It has also appeared on Alias and in Dan Brown's novels. Game developer Elonka Dunin is considered the leading expert on the sculpture, and Dan Brown apparently named a character after her (though he anagrammed and abbreviated the name to "Nola Kaye").
So, the unsolved text is still out there. Are you good at puzzles?