We recently released recent search, a Twitter API v2 endpoint that has similar functionality to this one. The new version is currently in development and serves adequate access for the majority of developers on our platform.
While elevated levels of access are coming to v2 soon, developers in need of higher levels of access can explore our v1.1 premium or enterprise APIs. You can see an overview of our search offerings on our search overview page, and see what's new with v2 by visiting the search comparison guide.
The Twitter's standard search API (search/tweets) allows simple queries against the indices of recent or popular Tweets and behaves similarly to, but not exactly like the Search UI feature available in Twitter mobile or web clients. The Twitter Search API searches against a sampling of recent Tweets published in the past 7 days.
Auth: Twitter Oauth 1.0, app-only or app-user
Query abilities: Limited operators for past ~7 days, recreating the search functionality in the Twitter UI. See How to build a standard query here.
Before digging in, it’s important to know that the standard search API is focused on relevance and not completeness. This means that some Tweets and users may be missing from search results. If you want to match for completeness you should consider the premium or enterprise search APIs.
A detailed reference on the standard search API endpoint can be found HERE.