This paper contributes to the philosophical foundations of conceptual modeling by addressing a number of foundational questions such as: What is a conceptual model? Among models used in computer science, which are conceptual, and which are not? How are conceptual models different from other models used in the Sciences and Engineering? The paper takes a stance in answering these questions and, in order to do that, it draws from a broad literature in philosophy, cognitive science, Logics, as well as several areas of Computer Science (including Databases, Software Engineering, Artificial Intelligence, Information Systems Engineering, among others). After a brief history of conceptual modeling, the paper addresses the aforementioned questions by proposing a characterization of conceptual models with respect to conceptual semantics and ontological commitments. Finally, we position our work w.r.t. to a “Reference Framework for Conceptual” modeling recently proposed in the literature.