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TrackBack was a protocol for web sites to notify other web sites when they've posted a link to them (respectively). It was a predecessor of pingback, which itself was a predecessor of the webmention protocol.
Trackback was first implemented in Movable Type v2.2, released 2002-06-26 . The Trackback specification was released in August 2002 by Six Apart. 
Trackback uses RDF in HTML comments to provide an unnecessarily complex (having to parse a completely different format) and fragile (HTML comments get stripped all the time in processing, e.g. by search engines) method of discovery. Pingback abandoned such methods, instead using an HTTP link header or link tag with rel for discovery.
Lack of link verification
Trackback "works" by a one-way HTTP request from the linker to the linkee, and the linkee is not expected to do any verification that the linker actually has a link to the linkee. Thus it was immediately overrun with spam and is considered useless. Pingback deliberately improved upon this by requiring verifying that the source links to the target.
Due to the lack of link verification, Trackback is particularly easy for spammers to overwhelm and thus has been largely abandoned due to being pretty much all spam at this point.
Posts Criticizing Trackback
- Trackback: A Tragedy in Three Acts antseyeview.com (2005)
- The Day the Trackbacks Died codinghorror.com (2006)
The Trackback spec doesn't appear to have any explicit implementation guidance for how to display trackback pings that have been received.
However, in practice CMS's display trackbacks in a section explicitly labeled "Trackbacks:", and for each such trackback ping:
- title of the post that sent the trackback
- ellipsed [...] ... [...] summary text, which is nearly unreadable without more context, and doesn't even show what phrase linked to the original blog post if any.
- the overall visual design is very dated and has fallen behind modern comment presentation designs
- capjamesg has implemented sending and receiving Trackbacks in the IndieWeb_Utils Python library.
- James is also working on a hosted Trackback server for personal use.
- Arxiv shows Trackbacks in the "blog links" associated with each paper.
- "Attention Is All You Need" paper: https://arxiv.org/abs/1706.03762
- Corresponding blog links: https://arxiv.org/tb/1706.03762
- Documentation on how Trackbacks on Arxiv work: https://info.arxiv.org/help/trackback.html