This paper provides an overview of the tools and methodologies for data privacy protection that can cope with the challenges raised by the Big Data storage and analytics processing, with focus on anonymity. Preserving individual privacy is one of the major issues in the context of Big Data, as while handling huge volumes of data, it is possible that sensitive or personally identifiable information ends up disclosed. In fact, even when dealing with anonymized raw data, sensitive information may be extracted through analytics. Preserving anonymity is particularly difficult because it should be done while allowing the analytics to produce useful insight about the data. We further discuss these challenges and future research directions in order to perform big data analytics in a privacy-compliant way.