The updates are taking a while to be rolled out to users, and some will not see any changes immediately.
Both new features allow users to search in real time on a topic of their choice. The Trends tab offers the top 10 topics being discussed on Twitter at any given time.
Users who already have access to the new features say that pop celebrity Chris Brown is currently in the lead.
Twitter has always had a search feature, but in a less obvious position at the bottom of the page. It was also necessary for users to leave their profile page in order to conduct a search.
In related news, low airfare provider Ryanair has been attacked by Twitter users. An account called '@RyanAirOnline', which is not officially owned by the airline, verbally abused customers visiting the profile page. The account has since been closed.
Ryanair, which holds a number of open accounts with Twitter to highlight fare offers, could not be reached for comment.
