In addition to “While you were away” this is also, surely, where Moments comes in to play. It has had its detractors from among the power users but I find it very useful to catch up. Following a specific moment in real time for its duration is also a joy and far more effective than following a hashtag which is often filled with spam. During the Super Bowl was a case in point.
Experienced, power users argue that Moments is not a needed addition – perhaps not if you are permanently living in your stream. I, however, think that Moments should be enhanced, given greater prominence and made easier to interact with, almost as though you are commenting on a story rather than sending a tweet.