Transparency and reproducibility in research methods and results are fundamental elements of research ethics and now widely considered as mandatory by funders, publishers, and the science community to warrant trust in science. Over the past years, much attention has been afforded by the international research community to define requirements for openly sharing data. There is broad consensus that data should be deposited in trustworthy repositories following the FAIR principles (Findable, Accessible, Interoperable, Reusable) for open data (https://www.force11.org/fairprinciples). Digital repositories should demonstrate trustworthiness through a standardized certification and accreditation process to ensure reliable management and durability (Diepenbroek et al. 2016: DSA-WDS Partnership Working Group Catalogue of Common Requirements). Samples are a fundamental part of research in the Geosciences, and transparent and reproducible research demands open access to samples. Can we transfer the FAIR principles for open data and standards for trusted repositories to the digital curation of samples? For example, the use of persistent and unique sample identifiers such as the IGSN (International Geo Sample Number) to unambiguous citation of samples requires a persistent virtual representation of the sample, to which it can resolve. Are online sample catalogs and registries trustworthy to fulfill this role? There is an urgent need to establish criteria for FAIR samples and for the trustworthiness of digital sample registries and catalogs based on what has already been developed for digital data repositories. In parallel, we need to ensure an infrastructure for the curation of the physical samples with trustworthy collections and repositories that fulfill criteria of reliability and persistence similar to those of digital repositories. This presentation is intended to ignite discussion on how to ensure trustworthy curation of samples both in the digital and in the physical world.