How do I do Complex Searches on Domain Names?

How to do complex searches on domain names, made simple:

On search boxes about domain names (Web and DNS reports), you can use a regular expression by prefixing the entry with a tilde character (~). For example, you can use this to filter all but some names. Here is a valid input to filter all but Google’s and Amazon’s:

~^(?!(.*\.)?google\.[fr|com]$)(?!.*amazon(\..{2,3}){1,2}$)