For those interested in true Docker-in-Docker, Nestybox is developing a solution that enables running Docker inside a Docker container **without using privileged containers** (i.e., much more securely).

More generally, Nestybox enables deployment of “system containers” with Docker. System containers are containers that run system-level workloads in them (such as Docker itself) that normally don’t run in regular containers.

There is a free demo at www.nestybox.com, and a blog article on this at https://blog.nestybox.com/2019/09/13/dind.html.