In principle facts and reports of facts (which is what most tweets are) are explicitly exempted from copyright protection in the majority of national and international copyright provisions. Hypothetically, however, content uploaded in Twitter might fall under the definition of intellectual property. A creative tweet for instance might qualify for copyright protection due to its originality and artistic nature. Consequently, the author of the tweet will automatically receive exclusive moral and economic rights over the tweet.
According to Twitters’ Terms and Conditions, when sharing any copyright content on Twitter users retain their rights to the shared content (which includes not only tweets but shared photos and videos as well). By submitting, posting or displaying this content to Twitter, however, users agree to grant the platform a worldwide, non-exclusive, royalty-free license (with the right to sublicense) to use, copy, reproduce, process, adapt, modify, publish, transmit, display and distribute the work in any and all media or distribution methods (now known or later developed).
Put simply, this license authorizes Twitter to make your works available to the rest of the world and to let others do the same. Furthermore, by granting the license you waive any rights for compensation in your favour with respect to the activities Twitter undertakes with your work. What’s more, by accepting the license you warrant that all the rights, power and authority necessary to grant the rights in the license to the works in hand are actually your ownership and do not belong to someone else.
The extra-territoriality of such an agreement can collide with various national copyright provisions similarly to the case of Facebook’s world-wide license, commented before. Some of the provisions might render the license agreement partially or in whole null and void, which will strip Twitter off certain rights to use the user’s copyright content.
Of course, the legal agreement with Twitter can be terminated at any time by deactivating your accounts and discontinuing your use of the services of Twitter. By virtue of such a termination, your author’s rights over your artistic content will not bear any limitations and you will remain free to exercise them as you like.