Gmail is one of the most popular mail app and already have some features for advanced search, filter and labelling where you can do a lot of things over and above the usual features. Try them and see that many splendid features are already bundled there.
For serious and large volume mail users there are some popular add-ons which are commonly used by such Gmail users.
Some of these are as follows -
(1) Mailstrom - This app is helpful when large emails flood your inbox and you want to see them categorically at a glance to treat them for final action from your side. This categorisation in front of you gives a better and quick control on them.
(2) The email game - It is an interesting app which gives you opportunity to play the email game and earn points for clearing or answering or deciding on the emails quickly.
(3) Sanebox - This is an app which automatically groups emails in different categories as per their importance.
(4) Gmelius - It is a versatile app which can do many jobs like schedule emails to a later time, snooze messages to leave inbox and return at a designated time, add notes to emails, create email templates, block email trackers, automate copying contacts, automatically label outgoing emails etc.
(5) Clearbit connect - This app is helpful when one is interested in having emails of companies on a sidebar and more often uses them. One can search emails of companies also.
(6) Checker Plus for Gmail - This is an chrome extension and useful for handling multiple Gmail addresses at a time.
Knowledge is power.