With the emergence of cloud computing paradigms, secure data outsourcing has become one of the crucial challenges which strongly imposes itself. Data owners place their data among cloud service providers in order to increase flexibility, optimize storage, enhance data manipulation and decrease processing time. Nevertheless, from a security point of view, access control is a major challenge in this situation seeing that the security policy of the data owner must be preserved when data is moved to the cloud. Nonetheless, the lack of a comprehensive and systematic review motivated us to construct this reviewing paper on this research problem. Here, we discuss current and emerging research on privacy and confidentiality concerns in data outsourcing and pinpoint potential issues that are still unresolved.