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Ultra-dense networks (UDNs) provide an effective solution to accommodate the explosively growing data traffic of multimedia services and real-time applications. However, the densification of large numbers of static small cells faces many fundamental challenges, including deployment cost, energy consumption and control, and so on. This motivates us to develop software-defined space-air-ground integrated moving cells (SAGECELL), a programmable, scalable, and flexible framework to integrate space, air, and ground resources for matching dynamic traffic demands with network capacity supplies. First, we provide a comprehensive review of state-of-the-art literature. Then the conceptual architecture of SAGECELL is elaborated in detail, and the technological benefits are emphasized. Next, we present four typical application cases of SAGECELL. A case study is conducted based on real-world road topology to …