Help me understand?

I don't get exactly how a wastegate works. Internal/external. I know they keep the turbo from overboosting and making your motor go booom, but im still confused. Do wastegates divert exhaust gasses back into your exhaust system after bypassing the turbo or what.
I always see the dial external wastegates on the manafold but don't see any pipe travelling from the wastegate back to the exhaust system. Am i just not lookin hard enough or what?

 

You've got the idea. The wastegate opens at a specified boost pressure to slow down the turbine blades. On most internals don't see where it connects back to the exhaust because it's just a valve that usually dumps into the downpipe. On externals though, there is a separate pipe that connects to downpipe. As far as you not seeing it on the external setups, look at more pics from more angles

 

sometimes you wont see the wastegate dump exiting into the exhaust, becuase sometimes they exit into the atmosphere (open dump)