The "hard" problem of strong of interactions

This is a write-up of a lecture at the level of a physics colloquium. There exists an idealized mathematical formulation of strong interactions which has no free parameters but is known to describe the real world quite accurately. Over the last three decades the problem has been managed with increasing success. An overview of some facts and a little fiction will be presented, but the question whether the problem can now be considered "easy" will be left unanswered.