The heated 5G network deployment race has already begun with the rapid progress in standardization efforts, backed by the current market availability of 5G-enabled network equipment, ongoing 5G spectrum auctions, early launching of non-standalone 5G network services in a few countries, among others. In this paper, we study current and future wireless networks from the viewpoint of energy efficiency (EE) and sustainability to meet the planned network and service evolution toward, along, and

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... d 5G, as also inspired by the findings of the EU Celtic-Plus SooGREEN Project. We highlight the opportunities seized by the project efforts to enable and enrich this green nature of the network as compared to existing technologies. In specific, we present innovative means proposed in SooGREEN to monitor and evaluate EE in 5G networks and beyond. Further solutions are presented to reduce energy consumption and carbon footprint in the different network segments. The latter spans proposed virtualized/cloud architectures, efficient polar coding for fronthauling, mobile network powering via renewable energy and smart grid integration, passive cooling, smart sleeping modes in indoor systems, among others. Finally, we shed light on the open opportunities yet to be investigated and leveraged in future developments.