Green computing and energy-saving have been important and hot research topics in mobile computing and cloud computing. In the recent years, many existing research results have been published to address energy saving issues and challenges in cloud computing or mobile computing. Today, the significant increase of mobile users and strong business interests in cloud computing and services drive an emergent opportunities and needs in mobile cloud computing. This brings a new attention to energy saving in mobile cloud computing and services. This paper first presents the research scope and classified issues in energy saving in mobile clouds. Then, it reviews the existing research results and techniques, and examines their strengths and weaknesses. Finally, the paper offers observations, and identifies the open issues and needs for future research.