There's an update to the official Twitter app for iOS. The new version 3.2 adds push notifications, so you can be pinged whenever someone mentions your Twitter handle, and also adds full support for iOS 4.2.
On the iPad, there are UI improvements that include panel animation and a dismiss feature. You can manage saved searches, and media can now be viewed inline.
The iPhone client provides additional Retina Display graphics, geotagging with just one tap, and improved display of shortened URLs.
Twitter for iOS remains free -- you can download it right now on the App Store.
Apple iPad Air 2
Apple iPhone 6