Security and privacy issues are magnified by the volume, variety, and velocity of big data, such as large-scale cloud infrastructures, diversity of data sources and formats, the streaming nature of data acquisition and high volume inter-cloud migration. In the past, big data was limited to very large organizations such as governments and large enterprises that could afford to create and own the infrastructure necessary for hosting and mining large amounts of data. These infrastructures were typically proprietary and were isolated from general networks. Today, big data is cheaply and easily accessible to organizations large and small through public cloud infrastructure. The purpose of this chapter is to highlight the big data security and privacy challenges and also presents some solutions for these challenges, but it does not provide a definitive solution for the problem. It rather points to some directions and technologies that might contribute to solve some of the most relevant and challenging big data security and privacy issues.