Twitter has enhanced is search feature, and has added all public tweets (from its inception in 2006) to its search engine. Historically, Twitter search results produced primarily “real-time” results, including tweets dating back about one week.
There is simply a ton of data that can be searched; more than 100 times the one week of search results. To see the history of tweets view “ALL” under the search results tab. Additionally, you can use the advanced search to search for phrases from (or to) a specific Twitter account. And, a bonus feature is being able to save your advanced search results to access at a later time.