Aviation is undergoing a paradigm shift to become a more sustainable industry. Priorities include reducing fossil fuel consumption, cutting carbon dioxide and other emissions, and developing new technologies. One of the major enabling technologies is the electrification of aircraft. Batteries are a key part of this revolutionary concept. This paper aims to provide key insights into battery technology and its potential to electrify aviation. Therefore, it proposes a comprehensive presentation of this technology following a detailed research process. Five different topics are addressed. The first is a general overview of the chemistry of electrochemical cells, the basic element of batteries. This is followed by a presentation of some of the most relevant previous work in this topic, highlighting their contributions and their main outcomes to be considered in further research. The main performance metrics used to compare the different batteries are presented next. For each of them, the definition, and related requirements that batteries used in electric aviation must meet are included. The paper then analyzes the possibilities for battery use in aviation and identifies some key challenges that need to be overcome to scale-up this technology. Finally, some battery technologies, their current uses, and their potential for further progress toward a more sustainable aviation are presented in detail.