The heterogeneous cellular network (HCN) is most significant as a key technology for future fifth-generation (5G) wireless networks. The energy efficient design of HCNs consist of different types of base stations (BSs), which has drawn significant attention to technologies for future 5G wireless networks. The cellular networks have faced a great deal of challenges to meet sharply rising demand for higher network capacity and higher data rates as well as far more power consumption which results in operating costs caused by the number of users accessing the cellular networks concurrently. BS is the main part of power consumption, so reducing energy consumption of the BS can obviously reduce the total energy consumption. Recently, the power consumption of the BSs has been attracted in cellular networks. In this chapter, we propose switching off/on systems for the efficient power consumption at the BSs in the cellular networks which introduce active/sleep modes in the macro BSs (MBSs) and femto BSs (FBSs). The active/sleep modes reduce the interference and power consumption as well as improve the energy efficiency of the cellular networks. Moreover, we derive the two-tier HCNs under different sleeping policies as well as formulate power consumption minimization for the MBSs and FBSs. An optimization problem is formulated to maximize the energy efficiency subject to throughput outage constraints as well as solved by the Karush-Kuhn-Tucker (KKT) conditions in terms of the femto tier BS density. Furthermore, the energy efficiency of cellular network is analyzed and modeled based on Markovian wireless channels.