Every field should have its Grand Challenges. After discussing some general "why and how" issues, with brief reference to some sample challenges, we devote attention to the challenges raised by the new world of "BigData" and to some new ways of approaching the classic Grand Challenge of the Holy Grail (where one merely states the problem and the computer solves it). There can, of course, never be a definitive catalogue of Grand Challenges. The ultimate Grand Challenge is for everyone working on Constraint Programming to look up on occasion from their everyday pursuits to consider how they might contribute to a Grand Challenge, and even to try their hand at formulating their own Grand Challenges.