In the lecture Battery and Fuel Cell Systems the topics covered in the lecture Batteries and Fuel Cells are deepened, current developments are presented and especially the system-relevant aspects of the technologies are dealt with. In the first part of the lecture fuel cell systems and their components are discussed. The integration of the different low- and high-temperature fuel cell types into systems is discussed, the different requirements for fuel preparation are presented and the system concepts implemented so far are compared. In the second part of the lecture, battery systems for hybrid and electric vehicles are presented and the batteries and cells used in them are discussed. The main focus is on lithium-ion battery systems. Charging strategies and circuits for charge balancing, safety concepts on cell and battery level as well as BMS systems are discussed. In the last part of the lecture, alternative electrochemical energy storage systems such as redox flow batteries and electrolysers are presented.