Sony’s PlayStation Network, including the PlayStation Store, is fully functional in North America, which Sony announced in a press release on June 2. There still seem to be a few bugs that need working out, but full service is online again, as is Sony’s Music Unlimited over all platforms.
These services are also running in Europe and certain parts of Asia, excluding Hong Kong, Japan and South Korea though Sony has promised to make further announcements when the down regions regain service.
While the press release was short and to the point, the PlayStation.Blog has a full list of details, including featured and discounted games and DLC as well as featured themes and avatars.
Update: The Welcome Back package is now active. Please visit Sony’s PlayStation.Blog here for all the details and instructions you will need to collect your swag.