Future mobile cellular networks will be characterized by massive densification of base stations (BSs) and a reshape of network functionalities, which include the potentials of advanced technologies like the network function virtualization, network slicing, and resource sharing among multiple operators. In the legacy networks, sleep-mode strategies have been proven to significantly increase the network energy efficiency.In this dissertation, BS sleep-mode schemes are formulated and proposed for the two most prevalent ultra-dense network types in the 5G mobile cellular networks. First, a multi-operators cellular network, where BSs are closely located is considered. Sleep-mode with Efficient Beamformers and Spectrum-sharing (SEBS) strategy, which minimizes BS power consumption of cooperative multi-operators is proposed. The licensed bandwidth of each operator is partitioned into private and shared bands to avail the active BSs sufficient spectrum resources for the support of all UEs. A mobile edge computing network is also considered, where densely deployed BSs are equipped with computation resources to process users offloaded computation-intensive tasks. In order to jointly tackle the issue of power consumption and latency interplay, the active number of BSs, uplink and downlink beamforming vectors, computation resource allocation, and task completion latency are formulated as an optimization problem, with the aim of reducing the network power consumption while satisfying the latency requirement. To efficiently solve the resulting joint optimization problem, a framework that first selects the active BSs based on communication and computation power-aware selection rule is proposed, and thus the remaining BSs can be switched off. The computation resources and dual-link beamformers are subsequently optimized for further network energy savings.The proposed energy efficiency strategies in this dissertation are endowed with active BSs selection, beamforming vectors optimization, latency minimization and bandwidth sharing, which makes this research applicable to various cellular network types. Therefore, this research will provide important insights into the development of energy efficiency strategies of future mobile cellular networks.