The legal framework on data protection in Europe sets a high standard with regard to the possible re-use of personal data. Principles like purpose limitation and data minimization challenge the emerging Big Data paradigm, where the "value" of data is linked to its somehow still unpredictable potential future uses. Nevertheless, the re-use of data is not impossible, once they are properly anonymized. The EU's Article 29 Working Party published in 2014 an Opinion on the application of anonymization techniques, which can be implemented to enable potential re-use of previously collected data within a framework of safeguards for individuals. The paper reviews the main elements of the Opinion, with a view to the widespread adoption of anonymization policies enabling a fair re-use of data, and gives an overview of the legal and technical aspects related to anonymization, pointing out the many misconceptions on the issue.