I've bought many iPhone apps by now, some free and some paid. I've reinstalled my computer, and in the new installation, iTunes is completely blank. On first sync, iTunes downloads the apps that are currently installed on my iPhone. But what about all those apps that I have bought and aren't currently installed?

Is there a way to re-download all my apps into iTunes?
Where can I see a listing of all the apps I've ever downloaded?

(Update: Apparently not all purchased content is restored - some things are inexplicably missing. You won't be charged anew for downloading them again, but you also won't be told what it is that you're missing. See here for details...)