This is a question that gets asked a number of times here at V7N. So here's the answer(s) from reputable SEO writers.
First up Rand Fishkin:
Which Page Markup + Tags Still Matter for SEO?
Should you focus on perfecting your H1s and H2s, or should structured data demand all your on-page attention? While Google hasn't completely pulled the rug out from under us, don't let the lack of drastic change in page markup fool you. In today's Whiteboard Friday, Rand outlines where to focus your efforts when it comes to on-page SEO and offers some tools to help with the process.
December 2nd, 2016 - Rand Fishkin Moz Blog