My wife's new-to-her 2011 Hyundai Elantra connects perfectly fine with my iPhone 4 and will pick up the phone and play music through the car's audio system. But there's absolutely no ability to control the playback from the car's controls. There's supposed to be, but it simply doesn't work.
I don't know if the CA and US spec Elantra is different, but
this guy claims AVRCP profile isn't included on the non-NAV models. So, if that's what you have, not being able to use the car's buttons to control the iPhone is exactly how it's supposed to work.
In my case, the JVC head in my Saab and Suzuki supports AVRCP 1.3 and both cars have steering wheel controls hooked up to the head unit. I can skip, reverse, and pause playback from either the steering wheel controls, the JVC touchscreen, or the phone itself. Those functions also work in 3rd party music apps such as Pandora and Slacker. Needless to say, it's very convenient when the phone is in your pocket.
EDIT: Link in above post is actually about 2011 Sonatas. It may not relate to the Elantra.