Flipboard, the social magazine iPad app that organizes sectionalized content (like “News,” “Technology” and “Food”) and social network updates into a sleek, unified interface, launched its highly anticipated iPhone app today. With the roll out, Flipboard announced a new feature called Cover Stories, which, according to CNET, “learns from a reader’s interactions with the content and helps them quickly catch up with some of the most interesting news, updates, and photos being shared at that moment.”

The new app easily translates the intuitive gestures that make the iPad version so enjoyable into those friendlier for the small screen: instead of horizontally swiping to turn pages, the iPhone version allows vertical swiping, which makes it much easier to navigate on the smaller device.

As Poynter writes, “Flipboard’s redesign for the smaller screen offers lessons in how publishers should tailor apps for the different needs of tablet and smartphone owners.” This includes the elimination of scrolling and intuitive navigation, among other important design lessons.

You can get the Flipboard for iPhone app in the iTunes store, though according to the Flipboard blog, it has seen its share of service issues today due to “high demand.”