Conventional cellular systems are designed to ensure ubiquitous coverage with an always present wireless channel irrespective of the spatial and temporal demand of service. This approach raises several problems due to the tight coupling between network and data access points, as well as the paradigm shift towards data-oriented services, heterogeneous deployments and network densification. A logical separation between control and data planes is seen as a promising solution that could overcome these issues, by providing data services under the umbrella of a coverage layer. This article presents a holistic survey of existing literature on the control-data separation architecture (CDSA) for cellular radio access networks. As a starting point, we discuss the fundamentals, concepts, and general structure of the CDSA. Then, we point out limitations of the conventional architecture in futuristic deployment scenarios. In addition, we present and critically discuss the work that has been done to investigate potential benefits of the CDSA, as well as its technical challenges and enabling technologies. Finally, an overview of standardisation proposals related to this research vision is provided.