Switch observability is a new observability concept for switched systems with unknown switching signals that is useful in the context of fault detection and identification. This notion, as well as the related concepts of switching signal observability and switching time observability, are investigated and fully characterized both for switched ODEs and switched DAEs. Switch observability is particularly useful in the context of fault detection and identification. A corresponding observer is designed. Also, the new concepts are applied to some power network example in order to highlight their use.