This chapter builds the general theory of the UG–iconicity interface, which consists of two general principles, with the Functional Iconicity Complementation Hypothesis (FICH) defining when the interaction is activated, and the Uniform Structure Mapping Principle (USM), how this interaction is carried out. In general, if a functional void of UG prevents a semantic/conceptual relation from mapping to a structural relation properly and thus halts an otherwise well-formed process of clause-generation, iconicity is called in to help finish the task. Intricate interactions between UG and iconicity may happen under the regulation of the USM so that the solution remains UG-compliant (and therefore has a proper interpretation). The scarce literature on the UG–iconicity relation is reviewed to provide the context in which the interface theory in this book is positioned and evaluated. The specific theory of the UG–iconicity interface is also compared with familiar examples in biology for further validation.