A metamodel is a relatively simple model that approximates the behavior of one that is more complex. A common and superficially attractive way to develop a metamodel is to generate large-model data and use off-the-shelf statistical methods without attempting to understand the model's internal workings. This monograph describes research illuminating why it can be important to improve the quality of such metamodels by using even modest phenomenological knowledge to help structure them. These "motivated metamodels" may convey an understandable, if only approximate, story-i.e., an explanation. Further, even if they provide little or no improvements to average goodness of fit, motivated metamodels can be much better for supporting decisions. For example, if the modeled system could fail if any of several critical components fail, then motivated models can build in the requisite nonlinearity, whereas naive metamodels are misleading. Naive metamodeling may also be misleading about the relative "importance" of inputs, thereby skewing resource-allocation decisions. Motivated metamodels can greatly mitigate such problems. The work contributes to the emerging understanding of multiresolution, multiperspective modeling (MRMPM), as well as providing an interdisciplinary view of how to combine virtues of statistical methodology with virtues of more theory-based work.