The receiver has to be connected to your home network, and your phone has to be connected to the same network. I downloaded the Android app from the Google Play store (it's free); I'm sure the iPhone/iPad app is available from the App Store.
You can control the inputs, the volume, certain DSP and sound settings, pick songs to play from a (home) music server. I think that you can stream music straight to it from Android, but not sure about streaming services like rdio. It's free so why not just try the app out for yourself.
Don't buy the wifi adapter its too expensive. You can use a older router if you have one and flash it with DDWRT and make it a bridge. That's what I did. You can find tutorials online and it's fairly easy to do. I ended up using my old linksys blue router that had been sitting in the closet for years.. If you plan on going this route, check the ddwrt website to see if your router is supported. Also I use ps3mediaserver with my 1010. It makes accessing your music from your phone or tablet a lot faster.