The core of DWiki is a template expansion engine and a collection of (text) renderers; DWiki displays pages by figuring out what template to use and then rendering it out.
Renderers generate text based on the current context, such as the page that is being displayed. The most important (and largest) renderer is the wikitext renderer, which takes page content in DWiki's wiki text format and turns it into HTML.
Other renderers create things like the navigation 'breadcrumbs' up at the top of this page and and the page tools and last-modified lines at the bottom. Renderers generally create only the essential pieces of that information; surrounding text is created through template expansion. Renderers are hardcoded parts of DWiki and are thus written in Python.
Templates are text files; they get expanded by the template engine through a recursive process of applying template 'macros' to their text. Template macros can insert other (expanded) templates, insert text taken from context variables, and insert the results of renderers. A typical template might look like:
<html><head><title>${|wikititle|wikiname} :: ${page}</title></head>
<body> @{breadcrumbs} <br/>
@{wikitext}
<hr> #{footer.tmpl} #{site-sig.tmpl} </body> </html>
(the actual templates that render this DWiki are somewhat more complicated than that, but this shows the flavour.)
DWiki produces all pages this way. Displaying different types of pages (regular pages versus directories) and different views of the same page (such as the history view) is done by selecting a different starting template; the template (presumably) uses different renderers that the normal view.
Errors are also rendered using templates (if an appropriate template exists). This allows some error pages to reuse renderers as appropriate; for example, the no-such-page error template includes breadcrumbs just as regular pages do, as you can see at NoSuchPage.
Wart: the view source display is not done by a template: it just barfs the content out straight as plain text. One current limitation of renderers and templates is that they can't control the content-type, which is set in the HTML view core.
Wart: the mapping of view + file attributes to templates is currently hard-coded.
DWiki is divided into two components: the front end and the core. The front end receives raw HTTP requests, figures out if they are proper requests, and then passes them to the core to go through the core's processing. If the front end can detect that a HTTP request is not something that the core can handle, it rejects it immediately with a terse error.
Similarly, if the core encounters a processing error it throws an exception up to the front end, which logs it and generates another terse error.
It is the front end that can optionally serve static files; the core is not involved in that process.