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Computer models provide a powerful tool for reasoning about difficult problems. Most computer modeling to date has used a familiar strategy for creating models. Those details that matter most are represented as accurately as possible, and all details not central to the problem are simplified or omitted. This traditional use of computer models has helped with many problems, but those that combine significant complexity with deep uncertainty can make this classical strategy difficult to employ. In these circumstances, knowing which details matter is difficult-models are prone to be incomplete, leaving out details that could matter under some conditions. Parametric or even structural uncertainties remain implicit so that no matter how detailed a model we create, we cannot confidently rely on its predictions about the real system's behavior. For these hard problems, any model we construct is a flawed mirror, potentially deceiving as well as illuminating.