In a JSF backing bean (Managed Bean, Weld Bean, doesn't matter), I can get the context path the client is on by calling
FacesContext ctx = FacesContext.getCurrentInstance();
String path = ctx.getExternalContext().getRequestContextPath();
This gives me the path the client currently accesses, like /myapplication.
Is it also possible to get the current page, like /home.faces, and how?