I recommend reading the Resource Shelf's blog post Resource of the Week: The Twitter Archives from the Library of Congress & Google: The Facts As We Know Them for more information about how Twitter's digital archives will be acquired and made available to the public from The Library of Congress. It's also interesting to learn how this will differ from Google Replay.
I also recommend the post from the Archivist of The United States, Tweets: What We Might Learn From Mundane Details. Yes, it's mentioned near the end of the post from the Resource Shelf but I think it's definitely worth noting.