We understand this paper as a contribution to the “anatomy” of conceptual models. We propose a signature of conceptual models for their characterization, which allows a clear distinction from other types of models. The motivation for this work arose from the observation that conceptual models are widely discussed in science and practice, especially in computer science, but that their potential is far from being exploited. We combine our proposal of a more transparent explanation of the nature of conceptual models with an approach that classifies conceptual models as a link between the dimension of linguistic terms and the encyclopedic dimension of notions. As a paradigm we use the triptych, whose central tableau represents the model dimension. The effectiveness of this explanatory approach is illustrated by a number of examples. We derive a number of open research questions that should be answered to complete the anatomy of conceptual models.