Quote Originally Posted by Vegechan
I'm still sort of confused as to what it is the Rinnegan even does... I mean, I know that if all these other bodies have the Rinnegan then he can see through them, but as we've seen in Nagato's flashbacks, his Rinnegan was still very powerful before he got these other bodies.

So what does it allow them to do exactly?
It lets him use all six elemental chakra types. It lets him control other people's chakra in his immediate surroundings. Using those chakra transmission bars (the black piercings), he can extend this control's range. This is presumably how he animated dead bodies -- by transmitting his chakra into them.

I think these powers "explain" everything we've seen him do, but I might be missing something.