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The Europeans started putting them in relatively recently as well. British roads got a lot of them in the 50s and 60s.
They are excellent for moderate traffic loads. For tiny traffic densities it doesn't matter (you could have a bloke with a flag and it would do the job), and for high traffic densities they can lock some of the entries out completely for long periods. They rely on there being gaps in the traffic to work.
Multilane roundabouts are either spiralled (I dislike these but for big ones it can make sense) or you move across from the inside to the outside when you're preparing to exit. Typically if you're turning right (your left) you'd be in the inside lane, left the outside lane, and straight ahead either one will do and there's a bit of a fight to get off first :p.