Genetic data contain sensitive health and non-health-related information about the individuals and their family members. Therefore, adopting adequate privacy safeguards is paramount when processing genetic data for research or clinical purposes. One of the major legal instruments for personal data protection in the EU is the new General Data Protection Regulation (GDPR), which has entered into force in May 2016 and repealed the Directive 95/46/EC, with an ultimate goal of enhancing effectiveness and harmonization of personal data protection in the EU. This paper explores the major provisions of the new Regulation with regard to processing genetic data, and assesses the influence of such provisions on reinforcing the legal safeguards when sharing genetic data for research purposes. The new Regulation attempts to elucidate the scope of personal data, by recognizing pseudonymized data as personal (identifiable) data, and including genetic data in the catalog of special categories of data (sensitive data). Moreover, a set of new rules is laid out in the Regulation for processing personal data under the scientific research exemption. For instance, further use of genetic data for scientific research purposes, without obtaining additional consent will be allowed, if the specific conditions is met. The new Regulation has already fueled concerns among various stakeholders, owing to the challenges that may emerge when implementing the Regulation across the countries. Notably, the provided definition for pseudonymized data has been criticized because it leaves too much room for interpretations, and it might undermine the harmonization of the data protection across the countries.