Cloud computing is currently gaining enormous momentum due to a number of promised benefits: ease of use in terms of deployment, administration, and maintenance, along with high scalability and flexibility to create new services. However, as more personal and business applications migrate to the cloud, service quality will become an important differentiator between providers. In particular, quality of experience as perceived by users has the potential to become the guiding paradigm for managing quality in the cloud. In this article, we discuss technical challenges emerging from shifting services to the cloud, as well as how this shift impacts QoE and QoE management. Thereby, a particular focus is on multimedia cloud applications. Together with a novel QoE-based classification scheme of cloud applications, these challenges drive the research agenda on QoE management for cloud applications.