Was playing around with Webmentions this weekend on this site and since they hook into WP's native trackback/ping feature, I assumed they would just work with my theme – but I was wrong. I'm using Equity here (for no other reason than I'm most familiar with it), and I found that because of the way we pull Trackbacks/Pings in Equity by type will cause the Webmentions to not display.
/equity/lib/framework/comments.php, we check only if there are comments with a type of 'pings' before displaying:
If you want to utilize Webmentions in your Equity child theme, you can add this following bit of code to your theme to enable support:
What we do here is just add an additional action to the existing
equity_pings action hook that will query for the comment type of 'webmention'. You can then change the markup to style them a little different from other trackbacks.