What is the fit conceptual structure involved in conceptual metaphors? Divers authors provide a large number of terms to debate the issue. While domain is the most common term, many others are also employed, covering frame, image schema, cognitive model, idealized cognitive model, scene, schema, scenario, etc. The problem is compounded by the fact that the terms mean diverse things to diverse researchers. The main aim of the article is to generate some clarity in this terminological and theoretical confusion. It suggests that conceptual metaphors concurrently involve conceptual structures, or units, on four levels of schematicity: the level of image schemas, the level of domains, the level of frames, and the level of mental spaces. It calls the resulting framework the “multi-level view of conceptual metaphor.” The multi-level view of metaphor can provide us with insights into a number of problems that have been raised and discussed in the CMT literature. The article displays that the study of metaphor within such a framework can legitimately be pursued on the four levels of schematicity and that no level can be singled out as the only fit level of analysis.