I will report on joint work with Tristan Collins where we look at pairs (X,D) where X is a complex projective manifold and D is a divisor with simple normal crossings such that K_X+D is trivial. I will focus on two special cases. First, if D is smooth and ample, I'll explain that the geometry (X,D) behaves like the geometry of a Calabi-Yau manifold. Second, if D has two ample, proportional components, then the geometry of (X,D) is drastically different.