We provide in this paper a tutorial and a comprehensive survey of QoE management solutions in current and future networks. We start with a high level description of QoE management for multimedia services, which integrates QoE modelling, monitoring, and optimization. This followed by a discussion of HTTP Adaptive Streaming (HAS) solutions as the dominant technique for streaming videos over the best-effort Internet. We then summarize the key elements in SDN/NFV along with an overview of ongoing research projects, standardization activities and use cases related to SDN, NFV, and other emerging applications. We provide a survey of the state-of-the-art of QoE management techniques categorized into three different groups: a) QoE-aware/driven strategies using SDN and/or NFV; b) QoE-aware/driven approaches for adaptive streaming over emerging architectures such as multi-access edge computing, cloud/fog computing, and information-centric networking; and c) extended QoE management approaches in new domains such as immersive augmented and virtual reality, mulsemedia and video gaming applications. Based on the review, we present a list of identified future QoE management challenges regarding emerging multimedia applications, network management and orchestration, network slicing and collaborative service management in softwarized networks. Finally, we provide a discussion on future research directions with a focus on emerging research areas in QoE management, such as QoE-oriented business models, QoE-based big data strategies, and scalability issues in QoE optimization.