I use TweetDeck. It is a useful tool for following along during a Twitter chat as it allows you to build columns that help to keep track of the many different feeds, notifications, mentions, etc.
It can be difficult to check out the resources shared and keep up with it all. There are many methods for 'saving' the resources shared. Kelly Fitzgerald @LISDTechie uses the collections feature in TweetDeck to gather those resources to review at a later time. Here she offers advice about how to add a collection and start saving those wonderful resources people are sharing.
"Starting today, we are introducing the ability to create custom timelines in TweetDeck. Custom timelines, which were just announced, are a new type of timeline that you control by selecting the Tweets you want to include."