How to: a blog with custom layout, with content from my medium.com page?

I've seen many people (but can't find the URL again) having a personal blog (firstnamelastname.com) whose content comes from their medium page.

What are the common ways to use this? (without having to clone manually / copy/paste between a wordpress and medium)

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I know how to register a .com and how to host a blogging engine, but what are the common ways to autoreplicate medium.com/user's articles to the blog?