Back in the good ol' days of the Web, when you would send Tim Berners-Lee e-mail telling him about your new site and he would soon e-mail you back (saying, "Wow, that's great! I'll put it on my list!"), I helped to put the MIT student newspaper on the Web. We were using Quark XPress for formatting (and Atex on a PDP-11 for writing and editing, if anyone cares), and wanted a way to turn the stories from Quark format into HTML.
Our solution was to export the Quark file into what are known as "XPress tags," which are a sorta-XML markup representation of the formatting. We then ran a relatively primitive Perl program (written by Jeremy Hylton, now of Python fame) on the output, which turn it into HTML.
I haven't used Quark in nearly a decade, the Perl program is probably woefully out of date, and I find it hard to believe that Quark doesn't have a free "save to XML" or "save to HTML" option. But if you want, take a look at this link, which seems to be one of the few preserved copies out there.