Twitter, in its commitment to keep you updated on everything under the sun, has added push notifications to its mobile app for when you've been 'mentioned'. The microblog announced that whenever someone you follow's talked to you or about you, you'll receive an instant notification on your mobile phone. This allows you to have an almost streamlined conversation over Twitter. Of course, if you don't want people people to read your conversations, it's better to switch over to SMS.
In addition to receiving notifications for mentions, Twitter's also added instant notifications for direct messages on iPhones, similar to the feature on Twitter for Blackberry.