The evolution of current wireless access networks towards 5G and beyond is characterized, among others, by the provisioning of high-bandwidth services and by the capability of serving traffic of a large number of heterogeneous devices. Among the key approaches for provisioning high capacity in such networks, a prominent role is played by network densification. However, dense deployments of many small cell base stations imply huge investments, increasing both CAPEX and OPEX for the mobile network. Additionally, densification increases the amount of overprovisioned network resources, due to variability in traffic demand over space and time. One of the most promising approaches to address these issues is the moving network paradigm, which exploits vehicle-mounted small cell moving base stations. This allows taking advantage of the correlation between spatio-temporal patterns of users and of vehicles, in order to create a network that flexibly and naturally densifies whenever and wherever needed by “following” users, hence reducing the need for dense deployments of static base stations. In this chapter, we review the main motivations and drivers for integrating moving base stations into future cellular access networks, and we outline the overall network architecture resulting from such integration. Furthermore, we characterize some of the main open research issues which stand in the way of the practical feasibility of the moving network paradigm. Among these are questions such as how to efficiently manage network resources in a dynamic fashion, accounting for the dynamics of service demand as well as of the moving network infrastructure; how to mitigate interference effects; how to implement mechanisms for reliable wireless mobile backhaul, for the interconnection of moving base stations to the core of the network; and how to efficiently provision Multi-access Edge Computing (MEC) services in the moving network paradigm.