The General Data Protection Regulation (GDPR) became binding law in the European Union Member States in 2018, as a step toward harmonizing personal data protection legislation in the European Union. The Regulation governs almost all types of personal data processing, hence, also, those pertaining to biomedical research. The purpose of this article is to highlight the main practical issues related to data and biological sample sharing that biomedical researchers face regularly, and to specify how these are addressed in the context of GDPR, after consulting with ethics/legal experts. We identify areas in which clarifications of the GDPR are needed, particularly those related to consent requirements by study participants. Amendments should target the following: (1) restricting exceptions based on national laws and increasing harmonization, (2) confirming the concept of broad consent, and (3) defining a roadmap for secondary use of data. These changes will be achieved by acknowledged learned societies in the field taking the lead in preparing a document giving guidance for the optimal interpretation of the GDPR, which will be finalized following a period of commenting by a broad multistakeholder audience. In parallel, promoting engagement and education of the public in the relevant issues (such as different consent types or residual risk for re-identification), on both local/national and international levels, is considered critical for advancement. We hope that this article will open this broad discussion involving all major stakeholders, toward optimizing the GDPR and allowing a harmonized transnational research approach.