Data security and privacy issues are magnified by the volume, the variety, and the velocity of Big Data and by the lack, up to now, of a reference data model and related data manipulation languages. In this paper, we focus on one of the key data security services, that is, access control, by highlighting the differences with traditional data management systems and describing a set of requirements that any access control solution for Big Data platforms may fulfill. We then describe the state of the art and discuss open research issues.