Data is one of the most valuable assets for organization. It can facilitate users or organizations to meet their diverse goals, ranging from scientific advances to business intelligence. Due to the tremendous growth of data, the notion of big data has certainly gained momentum in recent years. 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 organizations collecting the big data may want to protect their outsourced data from the cloud. In this paper, we survey our research towards development of efficient and effective privacy-enhancing (PE) techniques for management and analysis of big data in cloud computing. We propose our 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 point out research issues that still need to be addressed to develop comprehensive solutions to the problem of effective and efficient privacy-preserving use of data.