The shift of the information access paradigm to a mobile platform motivates research in mobile application energy profiling to augment device battery lifetime. Energy profiling schemes estimate mobile application power consumption when it is executed on resource-constrained mobile devices. Accurate power estimation helps identify rogue applications to optimize mobile battery power usage. The lack of a comprehensive survey on mobile application energy profiling schemes that covers various energy profiling aspects, such as profiling granularity, types, measurement resources, and model flexibility, has motivated us to review the existing literature comprehensively. Application energy profiling schemes exploit either hardware-equipment or software-based solutions to track battery-draining behavior during application execution in mobile devices. This study comprehensively reviews state-of-the-art mobile application energy profiling schemes to investigate the strengths and weaknesses of existing schemes. We propose a detailed thematic taxonomy based on the extensive literature review on mobile application energy profiling to classify the existing literature. The critical aspects and related features of existing energy profiling schemes are examined through an exhaustive qualitative analysis. The significant parameters from the reported literature are also extracted to investigate commonalities and differences among existing schemes. Finally, several research issues in mobile application energy profiling are put forward that should be addressed to increase energy profiling strength.