The FAIR Model Catalog for Ontology-Driven Conceptual Modeling Research, commonly referred to as OntoUML/UFO Catalog, is a structured and open-source catalog that contains OntoUML and UFO ontology models. It was conceived to allow collaborative work and to be easily accessible to all its users. The goal of the OntoUML/UFO Catalog is to support empirical research in OntoUML and UFO, as well as for the general conceptual modeling area, by providing high-quality curated, structured, and machine-processable data on why, where, and how different modeling approaches are used. The catalog offers a diverse collection of models, created by modelers with varying modeling skills, for a range of domains and different purposes. The models are available in machine-readable formats (JSON and Turtle) and are accessible via permanent identifiers.