Auto-typography: is there a way to do it?

Is there a way to make Hugo output the HTML with proper typography formatting? I in particular want both English and Russian rules.

I want these changes applied, for example:

Source Markdown: “Прокрастинация” - лишь название для лени.
Final HTML: «Прокрастинация» — лишь название для лени.

Source Markdown: In the '60s, rock ‘n’ roll
Final HTML: In the ’60s, rock ’n’ roll

Some custom pre-processor, maybe?

No concept of custom pre-processors.

I think Blackfriday’s smartypants should cover both your cases. To configure angled quotes, either on site or page level:

[blackfriday]
angledQuotes = true

In a future version of Hugo you can even do this on a “per-language”, see https://github.com/spf13/hugo/pull/2303