Extended interphases are playing an increasingly important role in electrochemical energy storage devices and, in particular, in lithium-ion and lithium metal batteries. With this in mind we initially address the differences between the concepts of interface and interphase. After that, we discuss in detail the mechanisms of solid electrolyte interphase (SEI) formation in Li-ion batteries. Then, we analyze the methods for interphase characterization, with emphasis put on in-situ and operando approaches. Finally, we look at the near future by addressing the issues underlying the lithium metal/electrolyte interface, and the emerging role played by the cathode electrolyte interphase when high voltage materials are employed.