Android/iOS: Not everyone is checking Twitter throughout the day. If you aren't a frequent user of the microblogging network, then you might enjoy TweetsPie as it collects the "best" tweets from your recent timeline.
Sign in with your Twitter credentials and TweetsPie will show you the 21 best tweets from the last 600 in your timeline. It hasn't disclosed how it concludes what is "best", but a cursory check indicates that it's some formula based on retweets and favourites. You can also filter the results by the most popular of those tweets retweeted by people you follow.
You can tap on any tweet to see three additional details: the number of retweets and favourites (tapping on which performs that action), and a 'Hide User' tab. Tap that and tweets from that user will never show up in TweetsPie again.
The tweets show you the sender, their profile pic, time of sending and the full tweet, but TweetsPie doesn't support inline images. The biggest restriction? There isn't an option to reply to the user or even open the tweet in a browser window or another client. You're stuck -- apart from retweeting or favoriting, there's no way for you to interact with that tweet or user.
TweetsPie also has a widget for Android devices to quickly check the results. The app is available for iOS and Android, but if you want a similar service for desktop, then Qureet gets the job done too.