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.