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Simple, low-resolution models are needed for high-level reasoning and communication, decision support, exploratory analysis, and rapidly adaptive calculations. Analytical organizations often have large and complex object models, which are regarded as reasonably valid. However, they do not have simpler models and cannot readily develop them by rigorously studying and simplifying the object model. Perhaps the object model is hopelessly opaque, the organization no longer has the expertise to delve into the model's innards, or there simply is not enough time to do so. One recourse in such instances is statistical metamodeling, which is often referred to as developing a response surface. The idea is to emulate approximately the behavior of the object model with a statistical representation based on a sampling of base-model "data" for a variety of test cases. No deep knowledge of the problem area or the object model is required. Unfortunately, such statistical metamodels can have insidious shortcomings, even if they are reasonably accurate "on average." This monograph describes some of those shortcomings and proposes a way (motivated metamodeling) to do better, which amounts to drawing upon an approximate understanding of the phenomena at work (i.e., upon approximate theory) to suggest variables for and perhaps the analytical form of the metamodel. This approach is hardly radical, but it is quite different from what happens in normal statistical metamodeling. The quality of metamodels can sometimes be greatly improved with relatively modest infusions of theory.