Many scientists support Open Access publishing of their manuscripts. But is support for open access to the underlying research data as easy to achieve? Open Science is the general move towards open access to research results funded with public money. Several funding agencies are including Open Science as a requirement in their grants, among others the Marie Skłodowska-Curie Actions and actions funded by the European Research Council. Open access to research data will allow broad usage of data across disciplines. Since public money was used to pay for the research, why should data only be in the hands of a few? Open Science will also allow open verification of research results. But on the other side of this openness are questions related to the protection of scientific information, Intellectual Property Rights, privacy concerns, and security of data. This debate aims to highlight the pros and cons of Open Science and discuss the potential consequences to the scientific community.