Biobanks are necessary resources for the storage and management of human biological materials, such as biofluids, tissues, cells, or nucleotides. They play a significant role in the development of new treatments and the advancement of basic and translational research, especially in the field of biomarkers discovery and validation. The regulatory landscape for biobanks, which is necessary to safeguard both privacy and scientific discoveries, exhibits significant heterogeneity across different countries and regions. This article outlines the standards that modern biobanks should fulfill in the European Union (EU), including general, structural, resource, process, and quality requirements. Special attention is given to the importance of transparency and donor consent following the General Data Protection Regulation (GDPR) and the ISO 20387:2018, the international standard specifies general requirements for biobanks. A dedicated section covers the preparation of donor information materials, emphasizing consent for research involvement and personal data processing. The delicate balance between donors' privacy rights and scientific research promotion is also discussed, with a focus on the patenting and economic use of biological material-derived inventions and data. Considering these factors, it would be warranted to refine legal frameworks and foster interdisciplinary collaboration to ethically and responsibly expand biobanking.