In reply to Katherine Moss.

For this functionality there aren't a lot of options. I think the minimal set would be

Webmention plugin
Semantic Linkbacks plugin (optional, but greatly improves the amount of data and context of replies and reactions)

The backfeed of reactions from Twitter will require a free Brid.gy account connected to your Twitter account.

More details can be found here: Threaded Replies and Comments with Webmentions in WordPress. One change that has occurred since I wrote that piece is that comments added to your posts should now send their own webmentions automatically instead of needing to do it manually or to add the u-in-reply-to portion.

While it should all work even with a theme that doesn't have great microformats support, your results will obviously be better if your theme does microformats 2 well (examples include SemPress, Independent Publisher, etc.)

If you need help, feel free to touch base and we can set up some time to do a video conference call/screen share to troubleshoot any problems you may have.