Relying on the cloud for storing data and performing computations has become a popular solution in today’s society, which demands large data collections and/or analysis over them to be readily available, for example, to make knowledge-based decisions. While bringing undeniable benefits to both data owners and end users accessing the outsourced data, moving to the cloud raises a number of issues, ranging from choosing the most suitable cloud provider for outsourcing to effectively protecting data and computation results. In this paper, we discuss the main issues related to data protection arising when data and/or computations over them are moved to the cloud. We also illustrate possible solutions and approaches for addressing such issues.