People were asking how do I find all my tweets and getting no easy answer for a long time --- until Twitter introduced the personal tweets archive at the end of 2012.
The personal tweet archiving function allows you to download all of the tweets you have ever sent on Twitter and store them on your desktop, where they become browsable and searchable. Tweets that you can download include your retweets as well as any original messages you sent.
Twitter provides a special interface for searching the tweets in your archive, one that includes some ability to interact with old tweets, too. But your personal tweet archive comes in a zipped file and remains offline, it's not an active part of the online Twitter experience.
How to Download My Tweets Archive
You download your tweets through the Settings page on Twitter. Click the gear icon at the top of the Twitter menu and choose "Settings," then scroll to the very bottom of the settings page. The archive function is labeled "Your Twitter archive." It will offer an option called "Request your archive" for you to click.
When you click the button to activate your personal tweet archive, Twitter will email you instructions with a link to the web page where you can download your tweets. It may take a bit of time for Twitter to prepare your tweets for downloading, depending on how many tweets you've sent. But eventually, you'll receive a link to the web page where you'll download a zipped file containing all your old messages.
Searching All My Tweets
After you download your tweet archive, you'll have a variety of options for viewing them. They'll be available in two formats. One is the standard data format of CSV, which is readable in a spreadsheet.
The other is a special format similar to Twitter's user interface, which will allow you to view the tweets from within your Web browser and browse them based on the month and year you sent them. The Twitter-like interface also will let you search all your tweets using keywords, phrases and hashtags.
Twitter said in a blog post announcing the new archive function was phasing it in, so not everyone got the my tweets archive function available to them right away. But eventually the my tweets archive download button should eventually have appeared at the bottom of everyone's settings page, because it was made available to all users.