Data outsourcing is an emerging paradigm that allows users and companies to give their (potentially sensitive) data to external servers that then become responsible for their storage, management, and dissemination. Although data outsourcing provides many benefits, especially for parties with limited resources for managing an ever more increasing amount of data, it introduces new privacy and security concerns. In this paper we discuss the main privacy issues to be addressed in data outsourcing, ranging from data confidentiality to data utility. We then illustrate the main research directions being investigated for providing effective data protection to data externally stored and for enabling their querying. Categories and Subject Descriptors H.2.4 [Database Management]: Systems—Relational databases; H.2.7 [Database Management]: Database Administration—Security, integrity, and protection; H.3.3 [Information Storage and Retrieval]: Information Search and Retrieval—Query formulat...