Big data is the term that characterized by its increasing volume, velocity, variety and veracity. All these characteristics make processing on this big data a complex task. So, for processing such data we need to do it differently like map reduce framework. When an organization exchanges data for mining useful information from this big data then privacy of the data becomes an important problem. In the past, several privacy preserving algorithms have been proposed. Of all those anonymizing the data has been the most efficient one. Anonymizing the dataset can be done on several operations like generalization, suppression, anatomy, specialization, permutation and perturbation. These algorithms are all suitable for dataset that does not have the characteristics of the big data. To preserve the privacy of the large dataset an algorithm was proposed recently. It applies the top down specialization approach for anonymizing the dataset and the scalability is increasing my applying the map reduce frame work. In this paper we survey the growth of big data, characteristics, map-reduce framework and all the privacy preserving mechanisms and propose future directions of our research.