How should I highlight important text?

If there is visually emphasized text on your page, use <strong> for bold and <em> for italics. Using <b> and <i> tags for this purpose is not desirable because these tags were deprecated for emphasizing text and will not respect screen reader settings to pronounce text differently.

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 presenting content in DOM order and using semantic markup to introduce meaning into a web page.