Protecting privacy in Big Data is a rapidly growing research area. The first approach towards privacy assurance was the anonymity method. However, recent research indicated that simply anonymized data sets can be easily attacked. Later, differential privacy was proposed, which proved to be the most promising approach. The trade-off between privacy and the usefulness of published data, as well as other problems, such as the availability of metrics to compare different ways of achieving anonymity, are in the realm of Information Theory. Although a number of review articles are available in literature, the information - theoretic methods capacities haven’t been paid due attention. In the current article an overview of state-of-the-art methods from Information Theory to ensure privacy are provided.