The popularity of Kakuro in Japan is similar to that of the crossword in Britain.
The grid contains number clues, each of which is essentially a sum. The objective is to place digits in the answer cells that add up to each clue-sum.
Only the digits 1-9 are permitted. No digit may be used more than once in any sum. (The same digit may occur more than once in a row or column.)
See the Puzzler Encyclopedia for further details and an interactive tutorial.