This dissertation studies the design and optimization of applying mobile edge computing (MEC) in three kinds of advanced wireless networks, which is motivated by three non-trivial but not thoroughly studied topics in the existing MEC-related literature. First, we study the application of MEC in wireless powered cooperation-assisted systems. The technology of wireless power transfer (WPT) used at the access point (AP) is capable of providing sustainable energy supply for resource-limited user equipment (UEs) to support computation offloading, but also introduces the double-near-far effect into wireless powered communication networks (WPCNs). By leveraging cooperation among near-far users, the system performance can be highly improved through effectively suppressing the double-near-far effect in WPCNs. Then, we consider the application of MEC in the unmanned aerial vehicle (UAV)-assisted relaying systems to make better use of the flexible features of UAV as well as its computing resources. The adopted UAV not only acts as an MEC server to help compute UEs' offloaded tasks but also a relay to forward UEs' offloaded tasks to the AP, thus such kind of cooperation between the UAV and the AP can take the advantages of both sides so as to improve the system performance. Last, heterogeneous cellular networks (HetNets) with the coexistence of MEC and central cloud computing (CCC) are studied to show the complementary and promotional effects between MEC and CCC. The small base stations (SBSs) empowered by edge clouds offer limited edge computing services for UEs, whereas the macro base station (MBS) provides high-performance CCC services for UEs via restricted multiple-input multiple-output (MIMO) backhauls to their associated SBSs. With further considering the case with massive MIMO backhauls, the system performance can be further improved while significantly reducing the computational complexity. In the aforementioned three advanced MEC systems, we mainly focus on minimizing the energy consumption of the systems subject to proper latency constraints, due to the fact that energy consumption and latency are regarded as two important metrics for measuring the performance of MEC-related works. Effective optimization algorithms are proposed to solve the corresponding energy minimization problems, which are further validated by numerical results
