How should I highlight important text?

If there is visually emphasized text on your page, use `<strong>` for bold and `<em>` for italics. The main difference between using `<b>` and `<strong>` is that, the `<b>` tag  draws attention to text but does not convey any additional importance. Whereas the <strong> element is for content that conveys greater importance.

If the emphasis is purely for presentation for instance visually darkening or italicizing text, but you would not pronounce it differently; then use CSS font and font-weight properties to obtain the desired appearance.

For more information, the Accessible Web Academy course Sequence and Semantics includes in-depth discussion about assistive technologies present content in DOM order and using semantic markup to introduce meaning into a web page.