The availability of cloud services offered by different providers brings several advantages to users and companies, facilitating the storage, sharing, and processing of data. At the same time, the adoption of cloud services brings new security and privacy risks and challenges. As a matter of fact when leveraging cloud-based services for data storage and processing, data owners loose direct control on their data. Data and queries over them could then be at risk for both potentially improper exposure, compromising their confidentiality, or tampering, compromising their integrity. In this paper, we discuss the main issues to be addressed for guaranteeing data security and privacy in cloud-based storage and processing. We illustrate the different challenges to be considered and the research directions toward their solutions.