Representative Gabrielle Giffords is now breathing on her own, and her condition has been upgraded from critical to serious condition.
Only two other survivors of the Tucson shooting remain in the hospital, and both of their conditions have been upgraded to good.
Very good news.
After the shooting, part of Giffords' skull was removed, which is a common strategy to prevent dangerous swelling in patients with traumatic brain injury. Once her brain has had more time to heal, that section of the skull will be replaced, which I imagine is the next big hurdle in her recovery. IIRC, CNN reported this weekend that would happen in the next couple of weeks.