Thread Arcs are a way to display even long and complex discourses in a compact way. Threadvis exemplifies this within the Thunderbird mail client.
Individual messages are represented by circular shapes here, which are aligned on a horizontal axis. Several types of messages are distinguished: normal vs. selected and by viewer or by others. Ownership (me vs. others) is indicated by shape variation, i.e. a hollow disc (a concept that could be extended for forums with different user roles like Moderator or message types like question / answer / comment / support / counter-argument …).
Highlighting messages is done with color or opacity; it also applies to the arcs which show the reply relationships. Unlike seen here, arcs are traditionally half-circles, but it makes sense to flatten them for GUIs so that all have very similar height. It helps to take advanced of top and bottom sides so the human eye can form continuous oscillating lines.
Color may be employed to distinguish different authors when there’s not enough room to show user names or avatar pictures. Arc length can show temporal distance, which may make sense to be scaled logarithmically. In the variant shown, there’s no indication of topic/subject changes.
Thread Tree is the traditional approach that accurately shows reply hierarchy but not chronology. They come as either Tree Diagram a or, more frequently, as (collapsible) Tree Table b, e.g. in Microsoft Outlook (Express) as far as I remember.
Thread Trees can be displayed spatially more efficiently if reply edges alternate between vertical and horizontal alignment. I don’t know whether this design pattern has an established name.
Apple Mail on the other hand supports only Conversations for grouping messages. They are always sorted chronologically regardless of reply relations. Twitter is similar, but
@mention is based on people, not messages. Classic chat clients cannot even do that much.
Most of these can also be adapted to visualize thread structure when showing the actual text and metadata (author, title …). For a blog, for instance, I can see nested Conversations as being worth a try, i.e. comments on the original article would be listed (anti-)chronologically in the vertical dimension below the blog posting and each of these major comments could have minor sub-comments that would chronologically show right of it. Thread Arcs wouldn’t work that well in this scenario, though, since they work best as a detached overview at a fixed position.