iOS and Android in North America. As for Euro twiddlers, unless they have an Android device they may have to wait until nearer November 29, when the console launches on that side of the ocean.
North Americans still have to wait until Friday to check out of the app's PS4-based features, such as providing a screen-based keyboard for the console, or a second SmartGlass-like screen for certain PS4 games. In the meantime, there's always things like text chat with PSN friends, trophy comparisons, profile viewing, game alerts, and PS Store browsing to keep you occupied. When the console does arrive on November 15, PS4 owners will be able to use the app to download purchased content directly to their new black box.
Also, one very useful thing the app links to is the console's web-based user manual. As it happens, we can do that too.