Cloud computing is a key technology for storing, managing and analyzing big data. However, such large, complex, and growing data, typically collected from various data sources, such as sensors and social media, can often contain personally identifiable information (PII) and thus the organization collecting the big data may want to protect their outsourced data from the cloud. In this talk, we will discuss current research towards development of efficient and effective privacy-enhancing (PE) techniques for management and analysis of big data in cloud computing. In particular, we will discuss initial approaches to address two important PE applications: (i) privacy-preserving data management and (ii) privacy-preserving data analysis under the cloud environment. Additionally, we will discuss research issues that still need to be addressed to develop comprehensive solutions to the problem of effective and efficient privacy-preserving use of data.