Résume  Large cardinals have minimal, canonical models. (This is a fact up to a point and a conjecture beyond that point.) These models are minimal in the sense that if a theory is consistencywise stronger than a large cardinal, then (empirically) that theory proves the existence of the minimal model for that large cardinal. However, it is somewhat more involved to say in which way these models are canonical. Their canonicity is witnessed by socalled iteration strategies. In my talk, I will try to explain what an iteration strategy is, how it witnesses the canonicity of a minimal model, and (if time permits) what is the modern approach to the study of these central objects.
