In 2022, over half of the web traffic was accessed through mobile devices. By reducing the energy consumption of mobile web apps, we can not only extend the battery life of our devices, but also make a significant contribution to energy conservation efforts. For example, if we could save only 5% of the energy used by web apps, we estimate that it would be enough to shut down one of the nuclear reactors in Fukushima. This paper presents a comprehensive overview of energy-saving experiments and related approaches for mobile web apps, relevant for researchers and practitioners. To achieve this objective, we conducted a systematic literature review and identified 44 primary studies for inclusion. Through the mapping and analysis of scientific papers, this work contributes: (1) an overview of the energy-draining aspects of mobile web apps, (2) a comprehensive description of the methodology used for the energy-saving experiments, and (3) a categorization and synthesis of various energy-saving approaches.