Wiktionary
n. A type of crossword involving wordplay and misleading definitions.
Wikipedia
Cryptic crosswords are crossword puzzles in which each clue is a word puzzle in and of itself. Cryptic crosswords are particularly popular in the United Kingdom, where they originated, Ireland, Israel, the Netherlands, and in several Commonwealth nations, including Australia, Canada, India, Kenya, Malta, New Zealand, and South Africa. In the United States, cryptics are sometimes known as "British-style" crosswords. Compilers of cryptic crosswords are commonly called "setters" in the UK.
Cryptic crossword puzzles come in two main types: the basic cryptic in which each clue answer is entered into the diagram normally, and the advanced or "variety" cryptic, in which some or all of the answers must be altered before entering, usually in accordance with a hidden pattern or rule which must be discovered by the solver.
Usage examples of "cryptic crossword".
He went back to the cryptic crossword from the Times of London, pondered, made another entry, erased an earlier one, then set the puzzle aside.
Through this, Williams, the languid typesetter, peered up at intervals from the vast cryptic crossword he was composing to catch the latest philippic directed towards a certain newly arrived police inspectre.
Nell could crack the Guardian cryptic crossword in under quarter of an hour on a good day.
In their more romantic days, one of the things Cade and Marie had liked doing together was solving cryptic crossword puzzles.