Q: How do I see the devices attached to my network through my airport extreme router?

I can't find a way to see the addresses of all the devices connected to my Airport Extreme base station over ethernet.  I can see the wifi clients attached to the Extreme and to each Airport Express in the network.  But I don't see any of the 15+ other ethernet-connected devices.  There does not seem to be any interface that get me to this list of devices or allows me to inspect or monitor their settings.  What am I missing?  How can you manage a network with this router without this capability?