This week, twitter is to roll out an interactive and real-time notification alert for the users for any engagement to their account. So now you will receive any real-time alert to every engagement to your tweets such as replies, favorite, or retweets. These notifications will be different from the others that you receive via email or the mobile apps.
Including the replies and retweets, a user will also receive the alerts for new follower and direct message. But to get notifications you have to change the current notification setting and chose which notifications you want to see.
The company is working on a wide array of features that are expected to come handy for its users