Timelines: Timelines are collections of Tweets, ordered with the most recent first.
Tweets: Tweets are the atomic building blocks of Twitter, 140-character status updates with additional associated metadata. People tweet for a variety of reasons about a multitude of topics.
Search: Find relevant Tweets based on queries performed by your users.
Direct Messages: Direct Messages are short, non-public messages sent between two users. Access to Direct Messages is governed by the The Application Permission Model.
Friends & Followers: Users follow their interests on Twitter through both one-way and mutual following relationships.
Users: Users are at the center of everything Twitter: they follow, they favorite, and tweet & retweet.
Suggested Users: Categorical organization of users that others may be interested to follow.
Favorites: Users favorite tweets to give recognition to awesome tweets, to curate the best of Twitter, to save for reading later, and a variety of other reasons. Likewise, developers make use of "favs" in many different ways.
Lists: Lists are collections of tweets, culled from a curated list of Twitter users. List timeline methods include tweets by all members of a list.
Accounts: Account-level configuration settings for users.
Notification: Controls SMS-based notifications that a user wants to receive.
Saved Searches: Allows users to save references to search criteria for reuse later.
Local Trends: Allows users to save references to search criteria for reuse later.
Places & Geo: Users tweet from all over the world. These methods allow you to attach location data to tweets and discover tweets & locations.
Trends: With so many tweets from so many users, themes are bound to arise from the zeitgeist. The Trends methods allow you to explore what's trending on Twitter.
Block: Allows users to block and unblock other users.
Spam Reporting: These methods are used to report user accounts as spam accounts.
OAuth: Twitter uses OAuth for authentication. Be sure and read about Using OAuth 1.0a.
Help: These methods assist you in working & debugging with the Twitter API.
Legal: API Methods to address legal issues in your applications.