Source: http://gizmodo.com/5629243/twitter-adding-push-notifications-to-its-iphone-app
Twitter is currently in the final stages of testing push notifications in its iPhone app, pending a full activation of the feature in the next iOS release. According to TechCrunch, users with iOS 4.1 and its updated Twitter client will be able to enable the feature, bringing them closer still to the dream of full integration with the online hive mind. [TechCrunch]