The storage of electric energy is of ever growing importance for our modern, technology-based society, and novel battery systems are in the focus of research. The substitution of conventional metals as redox-active material by organic materials offers a promising alternative for the next generation of rechargeable batteries since these organic batteries are excelling in charging speed and cycling stability. This review provides a comprehensive overview of these systems and discusses the numerous classes of organic, polymer-based active materials as well as auxiliary components of the battery, like additives or electrolytes. Moreover, a definition of important cell characteristics and an introduction to selected characterization techniques is provided, completed by the discussion of potential socio-economic impacts.