Is there a smooth lattice polytope which does not have the integer decomposition property?

We introduce Tadao Oda's famous question on lattice polytopes which was originally posed at Oberwolfach in 1997 and, although simple to state, has remained unanswered. The question is motivated by a discussion of the two-dimensional case - including a proof of Pick's Theorem, which elegantly relates the area of a lattice polygon to the number of lattice points it contains in its interior and on its boundary.