From inside of a Docker container, how do I connect to the localhost of the machine?

If you are using Docker-for-mac or Docker-for-Windows 18.03+, 
just connect to your mysql service using the host host.docker.internal (instead of the 127.0.0.1 in your connection string).

If you are using Docker-for-Linux 20.10.0+, 
you can also use the host host.docker.internal if you started your Docker container with the --add-host host.docker.internal:host-gateway option.

Otherwise, read below