Controlled vocabularies and authority data are central to the reusability of data used to describe objects in museums and collections. The Minimum Record Recommendation for Museums and Collections already contains key guidance on terminology use in core elements of object documentation. This report presents a series of relevant vocabularies for collection documentation, including those suitable for specific documentation focuses and disciplines. Each one is assessed according to the criteria of the internationally recognised FAIR Principles, and a brief description is provided of the respective content focuses and the technical implementation status of the web offerings. This allows museum and collection professionals, as well as those who reuse datasets, to make an informed assessment of the sustainability of the described vocabularies in the context of linked publishing and effective research data management. This paper was prepared by a sub-working group of the Minimum Record Working Group of the Fachgruppe Dokumentation of the German Museum Association (DMB). The group comprises staff and representatives from the German Digital Library, the Humboldt- Universität Berlin (Coordination Centre for Scientific University Collections in Germany), the Institute for Museum Research, the Klassik Stiftung Weimar, the Ludwig-Maximilians-Universität Munich, Philipps-Universität Marburg (Deutsches Dokumentationszentrum für Kunstgeschichte - Bildarchiv Foto Marburg), and the Verbundzentrale des Gemeinsamen Bibliotheksverbunds Göttingen (VZG). It was developed as part of the NFDI consortia NFDI4Objects (https://www.nfdi4objects.net/; DFG project number 501836407) and NFDI4Culture (https://nfdi4culture.de/; DFG project number 441958017), as well as the joint project 'SODa – Collections, Objects, Data Competencies' (https://sammlungen.io/). We would like to thank the German Research Foundation (DFG) and the Federal Ministry of Research, Technology and Space (BMFTR) for their financial support. The German version of the report is available at https://doi.org/10.5281/zenodo.17950403.