The cloud computing paradigm has become a mainstream solution for the deployment of business processes and applications. In the public cloud vision, infrastructure, platform, and software services are provisioned to tenants (i.e., customers and service providers) on a pay-as-you-go basis. Cloud tenants can use cloud resources at lower prices, and higher performance and flexibility, than traditional on-premises resources, without having to care about infrastructure management. Still, cloud tenants remain concerned with the cloud’s level of service and the nonfunctional properties their applications can count on. In the last few years, the research community has been focusing on the nonfunctional aspects of the cloud paradigm, among which cloud security stands out. Several approaches to security have been described and summarized in general surveys on cloud security techniques. The survey in this article focuses on the interface between cloud security and cloud security assurance. First, we provide an overview of the state of the art on cloud security. Then, we introduce the notion of cloud security assurance and analyze its growing impact on cloud security approaches. Finally, we present some recommendations for the development of next-generation cloud security and assurance solutions.