According to the present data 0.5% of global energy is consumed by wireless networks. Energy efficiency is required for the environment and to lower the network operational cost. In this paper, we are about to discuss various methods of energy conservation in the heterogeneous cellular network. Energy consumption is reduced by self-organization algorithm and message passing algorithm by switching off-peak Base station controllers (BSC). Along with the increasing demands for cellular networks, the various problems for energy conservation in cellular networking have also increased. There are various models present which help in increasing the energy efficiency of cellular networking such as the Novel power consumption model and refined power consumption model. Also, an increase in the higher performance of cellular networks leads to an increase in energy consumption. In this paper, we are about to discuss various challenges which are faces for increasing energy efficiency and their solution.