Cloud Computing (CC) holds a new dawn of computing where multiple services are offered to the cloud users through internet. CC has a qualitative, flexible and cost effective delivery platform for providing services to IT users with the aid of internet. Due to advent of CC, capabilities of Mobile devices’ system has been improved. Mobiles devices can now depend on CC and information storage resources, to carryout complex computational operations which includes multimedia, searching and data mining. Also when considering local cloud, computation service is provided by enhancing operation of mobile cloud which handles mobile devices as a service nodes for example sensing services and computation of task. The task that need to be computed has to be offloaded to local or conventional cloud to ease battery power. The energy consumption during offloading of task is highly significant. Hence, characterization of some of the recent research works on battery energy in MCC are grouped into dynamic and non-dynamic energy-aware task offloading and a comparative analysis table are presented and finally open research issues are qualitatively discussed based on critical assessment of the literature