In recent years, big data have become a hot research topic. The increasing amount of big data also increases the chance of breaching the privacy of individuals. Since big data require high computational power and large storage, distributed systems are used. As multiple parties are involved in these systems, the risk of privacy violation is increased. There have been a number of privacy-preserving mechanisms developed for privacy protection at different stages (e.g., data generation, data storage, and data processing) of a big data life cycle. The goal of this paper is to provide a comprehensive overview of the privacy preservation mechanisms in big data and present the challenges for existing mechanisms. In particular, in this paper, we illustrate the infrastructure of big data and the state-of-the-art privacy-preserving mechanisms in each stage of the big data life cycle. Furthermore, we discuss the challenges and future research directions related to privacy preservation in big data.