Complex predictive models are notoriously hard to construct and to study. Without referring to the models directly -- only that a model consists of spaces and maps between them -- complex models can be assembled from smaller, easier-to-construct models. This talk will explain how a disciplined, diagrammatic process encodes continuous dynamical systems, partial differential equations, probabilistic graphical models, and discrete approximations of these models. Once encoded, a number of novel and powerful techniques are available; this talk will showcase several promising candidates.