Twitter has introduced a new capability that allows you to search for tweets by date range. Twitter keeps building in tools that previously required third party services. While it has been possible to do advanced searches on Twitter in the past, it was complicated and difficult to figure out. Twitter has made search much more user-friendly.
Twitter's advanced search makes it possible to search exact phrases, hashtags, places, accounts mentioned, and more in addition to date ranges. This is great for researching news stories or commentary from a particular point in time. The new search page is at twitter.com/search-advanced.