Twitter has two "native" ways of coping with this situation, search and lists.
Search allows you to look for mentions of a specific hashtag (I look at #km periodically, for instance) or a specific person. It works very well, but of course you have to have a topic in mind before you begin.
Twitter lists allow you to group sets of followers and then watch the stream only from that subgroup. Among my lists is "legal-kmers", a group of tweeps I especially value because they are legal information professional like myself* and because they periodically post or link to valuable content.
Even at that level of specificity to my work, it's not easy to review the valuable posts that go by. That's where paper.li comes in. It allows you to point to a Twitter list and generate a newspaper-like view of all the links posted the previous day. The URL is simply paper.li plus your Twitter account name plus the name of the list, hence:
If you don't want to leave this page, here's what it looks like on a specific day.
What makes it newspaper-like is that it includes the headline and a small amount of content from the article or other site to which my legal kmer has linked. That's hugely valuable for helping me identify something that speaks to me. Paper.li also sorts the articles "below the fold" into somewhat vague categories like Education, Technology, Crime, and Business. It also shows a scrolling version of today's legal-kmers posts. If you log in with a paper.li or Twitter account, the posts are interactive (i.e., you can easily re-tweet). Finally, Paper.li includes daily archives, in case you want to go back and look at a previous date's posts.
All in all, paper.li is a great addition to my collection of tools to "tame the information firehose." Who are your favorite tweeps? Who consistently finds the good stuff? Put them in a list and share them with me!
*not all are formally legal knowledge managers, however.