The highly demanding Over-The-Top (OTT) multimedia applications pose increased challenges to Internet Service Providers (ISPs) for assuring a reasonable Quality of Experience (QoE) to their customers due to lack of flexibility, agility and scalability in traditional networks. The future networks are shifting towards the cloudification of the network resources via Software Defined Networks (SDN) and Network Function Virtualization (NFV). This will equip ISPs with cutting-edge technologies to provide service customization during service delivery and offer QoE which meets customers' needs via intelligent QoE control and management approaches. Towards this end, we provide in this paper a tutorial and a comprehensive survey of QoE management solutions in current and future networks. We start with a highlevel 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 QoEoriented business models, QoE-based big data strategies, and scalability issues in QoE optimization.