For a long time, I had my own blog at one place or another. For a while, it was just at explosion-pills.com, then I popped up ghost on a DigitalOcean droplet at blog.explosion-pills.com. Finally, explosionpills.com became available, and now blog.explosionpills.com redirects to this medium blog that you’re reading through CloudFlare.
I personally know a couple of people who use Medium as a blogging platform, and of course I follow a lot of famous or semi-famous people who blog directly on Medium. It has functionality that I can't take the time to implement in blogging software that I manage myself even if I think I could theoretically do it. Here, readers have access to comments, highlighting, and of course a broad network of content creators.