The Edge's guitar rig has expanded exponentially since the 80s' One thing that stayed constant throughout all these years is without a doubt his amps, the ac-30s.
I noticed they used Shure SM58s for vocals, at least for the Joshua Tree Tour.
The last 2 tours, Elevation and Vertigo, they used Shure Beta58s UHF wireless.
Thats the basics. It would take forever to go through all the stuff they changed, but look around in the forum, and you'll find plenty of info.